Готові списки джерел за темами / Quantum theory – Mathematics; Group theory

Добірка наукової літератури з теми "Quantum theory – Mathematics; Group theory"

Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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Статті в журналах з теми "Quantum theory – Mathematics; Group theory"

Murphy, G. J., and L. Tuset. "Aspects of compact quantum group theory." Proceedings of the American Mathematical Society 132, no. 10 (June 2, 2004): 3055–67. http://dx.doi.org/10.1090/s0002-9939-04-07400-3.

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Vitiello, Giuseppe. "Group Contraction in Quantum Field Theory." International Journal of Theoretical Physics 47, no. 2 (July 25, 2007): 393–414. http://dx.doi.org/10.1007/s10773-007-9461-8.

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Antoine, Jean-Pierre. "Group Theory: Mathematical Expression of Symmetry in Physics." Symmetry 13, no. 8 (July 26, 2021): 1354. http://dx.doi.org/10.3390/sym13081354.

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The present article reviews the multiple applications of group theory to the symmetry problems in physics. In classical physics, this concerns primarily relativity: Euclidean, Galilean, and Einsteinian (special). Going over to quantum mechanics, we first note that the basic principles imply that the state space of a quantum system has an intrinsic structure of pre-Hilbert space that one completes into a genuine Hilbert space. In this framework, the description of the invariance under a group G is based on a unitary representation of G. Next, we survey the various domains of application: atomic and molecular physics, quantum optics, signal and image processing, wavelets, internal symmetries, and approximate symmetries. Next, we discuss the extension to gauge theories, in particular, to the Standard Model of fundamental interactions. We conclude with some remarks about recent developments, including the application to braid groups.

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Lev, Felix M. "Symmetries in Foundation of Quantum Theory and Mathematics." Symmetry 12, no. 3 (March 4, 2020): 409. http://dx.doi.org/10.3390/sym12030409.

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In standard quantum theory, symmetry is defined in the spirit of Klein’s Erlangen Program—the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the definition should be the opposite—background space has a direct physical meaning only on classical level while on quantum level symmetry should be defined by a Lie algebra of basic operators. Then the fact that de Sitter symmetry is more general than Poincare symmetry can be proved mathematically. The problem of explaining cosmological acceleration is very difficult but, as follows from our results, there exists a scenario in which the phenomenon of cosmological acceleration can be explained by proceeding from basic principles of quantum theory. The explanation has nothing to do with existence or nonexistence of dark energy and therefore the cosmological constant problem and the dark energy problem do not arise. We consider finite quantum theory (FQT) where states are elements of a space over a finite ring or field with characteristic p and operators of physical quantities act in this space. We prove that, with the same approach to symmetry, FQT and finite mathematics are more general than standard quantum theory and classical mathematics, respectively: the latter theories are special degenerated cases of the former ones in the formal limit p → ∞ .

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Pollatsek, Harriet. "Quantum Error Correction: Classic Group Theory Meets a Quantum Challenge." American Mathematical Monthly 108, no. 10 (December 2001): 932. http://dx.doi.org/10.2307/2695416.

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Brzeziński, Thomasz, and Shahn Majid. "Quantum group gauge theory on quantum spaces." Communications in Mathematical Physics 157, no. 3 (November 1993): 591–638. http://dx.doi.org/10.1007/bf02096884.

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Brzeziński, T., and Shahn Majid. "Quantum group Gauge theory on quantum spaces." Communications in Mathematical Physics 167, no. 1 (January 1995): 235. http://dx.doi.org/10.1007/bf02099359.

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Strickland, Elisabetta. "Classical Invariant Theory for the Quantum Symplectic Group." Advances in Mathematics 123, no. 1 (October 1996): 78–90. http://dx.doi.org/10.1006/aima.1996.0067.

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Robinson, Derek W. "Commutator Theory on Hilbert Space." Canadian Journal of Mathematics 39, no. 5 (October 1, 1987): 1235–80. http://dx.doi.org/10.4153/cjm-1987-063-2.

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Commutator theory has its origins in constructive quantum field theory. It was initially developed by Glirnm and Jaffe [7] as a method to establish self-adjointness of quantum fields and model Hamiltonians. But it has subsequently proved useful for a variety of other problems in field theory [17] [15] [8] [3], quantum mechanics [5], and Lie group theory [6]. Despite all these detailed applications no attempt appears to have been made to systematically develop the theory although reviews have been given in [22] and [9]. The primary aim of the present paper is to partially correct this situation. The secondary aim is to apply the theory to the analysis of first and second order partial differential operators associated with a Lie group.

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BONAHON, FRANCIS. "QUANTUM TEICHMÜLLER THEORY AND REPRESENTATIONS OF THE PURE BRAID GROUP." Communications in Contemporary Mathematics 10, supp01 (November 2008): 913–25. http://dx.doi.org/10.1142/s0219199708003095.

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Дисертації з теми "Quantum theory – Mathematics; Group theory"

Gupta, Neha. "Homotopy quantum field theory and quantum groups." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/38110/.

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The thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one (Chapter 3) of the thesis generalises the definition of an n-dimensional HQFT in terms of a monoidal functor from a rigid symmetric monoidal category X-Cobn to any monoidal category A. In particular, 2-dimensional HQFTs with target K(G,1) taking values in A are generated from any Turaev G-crossed system in A and vice versa. This is the generalisation of the theory given by Turaev into a purely categorical set-up. Part two (Chapter 4) of the thesis generalises the concept of a group-coalgebra, Hopf group-coalgebra, crossed Hopf group-coalgebra and quasitriangular Hopf group-coalgebra in the case of a group scheme. Quantum double of a crossed Hopf group-scheme coalgebra is constructed in the affine case and conjectured for the more general non-affine case. We can construct 3-dimensional HQFTs from modular crossed G-categories. The category of representations of a quantum double of a crossed Hopf group-coalgebra is a ribbon (quasitriangular) crossed group-category, and hence can generate 3-dimensional HQFTs under certain conditions if the category becomes modular. However, the problem of systematic finding of modular crossed G-categories is largely open.

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Mantke, Wolfgang Johann. "Picture independent quantum action principle." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/29850.

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Carruth, Nathan Thomas. "Classical Foundations for a Quantum Theory of Time in a Two-Dimensional Spacetime." DigitalCommons@USU, 2010. https://digitalcommons.usu.edu/etd/708.

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We consider the set of all spacelike embeddings of the circle S1 into a spacetime R1 × S1 with a metric globally conformal to the Minkowski metric. We identify this set and the group of conformal isometries of this spacetime as quotients of semidirect products involving diffeomorphism groups and give a transitive action of the conformal group on the set of spacelike embeddings. We provide results showing that the group of conformal isometries is a topological group and that its action on the set of spacelike embeddings is continuous. Finally, we point out some directions for future research.

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Gajewski, David C. "Analysis of Groups Generated by Quantum Gates." Connect to full text in OhioLINK ETD Center, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1250224470.

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Cooney, Nicholas. "Quantum multiplicative hypertoric varieties and localization." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:17d0824f-e8f2-4cb7-9e84-dd3850a9e2a2.

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In this thesis, we consider q-deformations of multiplicative Hypertoric varieties, where q∈𝕂^x for 𝕂 an algebraically closed field of characteristic 0. We construct an algebra D_q of q-difference operators as a Heisenberg double in a braided monoidal category. We then focus on the case where q is specialized to a root of unity. In this setting, we use D_q to construct an Azumaya algebra on an l-twist of the multiplicative Hypertoric variety, before showing that this algebra splits over the fibers of both the moment and resolution maps. Finally, we sketch a derived localization theorem for these Azumaya algebras.

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Laugwitz, Robert. "Braided Hopf algebras, double constructions, and applications." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:ddcb459f-c3b4-40dd-9936-6bad6993ce8c.

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This thesis contains four related papers which study different aspects of double constructions for braided Hopf algebras. The main result is a categorical action of a braided version of the Drinfeld center on a Heisenberg analogue, called the Hopf center. Moreover, an application of this action to the representation theory of rational Cherednik algebras is considered. Chapter 1 : In this chapter, the Drinfeld center of a monoidal category is generalized to a class of mixed Drinfeld centers. This gives a unified picture for the Drinfeld center and a natural Heisenberg analogue. Further, there is an action of the former on the latter. This picture is translated to a description in terms of Yetter-Drinfeld and Hopf modules over quasi-bialgebras in a braided monoidal category. Via braided reconstruction theory, intrinsic definitions of braided Drinfeld and Heisenberg doubles are obtained, together with a generalization of the result of Lu (1994) that the Heisenberg double is a 2-cocycle twist of the Drinfeld double for general braided Hopf algebras. Chapter 2 : In this chapter, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf algebras which are of what we call weakly separable type, we obtain a class of pointed Hopf algebras which can be viewed as natural generalizations of multiparameter deformations of universal enveloping algebras of Lie algebras. These Hopf algebras are instances of a new version of braided Drinfeld doubles, which we call asymmetric braided Drinfeld doubles. This is a generalization of an earlier result by Benkart and Witherspoon (2004) who showed that two-parameter quantum groups are Drinfeld doubles. It is possible to recover a Lie algebra from these doubles in the case where the group is free and the parameters are generic. The Lie algebras arising are generated by Lie subalgebras isomorphic to sl2. Chapter 3 : The universal enveloping algebra U(tr_n) of a Lie algebra associated to the classical Yang-Baxter equation was introduced in 2006 by Bartholdi-Enriquez-Etingof-Rains where it was shown to be Koszul. This algebra appears as the A_n-1 case in a general class of braided Hopf algebras in work of Bazlov-Berenstein (2009) for any complex reection group. In this chapter, we show that the algebras corresponding to the series B_n and D_n, which are again universal enveloping algebras, are Koszul. This is done by constructing a PBW-basis for the quadratic dual. We further show how results of Bazlov-Berenstein can be used to produce pairs of adjoint functors between categories of rational Cherednik algebra representations of different rank and type for the classical series of Coxeter groups. Chapter 4 : Quantum groups can be understood as braided Drinfeld doubles over the group algebra of a lattice. The main objects of this chapter are certain braided Drinfeld doubles over the Drinfeld double of an irreducible complex reflection group. We argue that these algebras are analogues of the Drinfeld-Jimbo quantum enveloping algebras in a setting relevant for rational Cherednik algebra. This analogy manifests itself in terms of categorical actions, related to the general Drinfeld-Heisenberg double picture developed in Chapter 2, using embeddings of Bazlov and Berenstein (2009). In particular, this work provides a class of quasitriangular Hopf algebras associated to any complex reflection group which are in some cases finite-dimensional.

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Majard, Dany. "Cubical categories, TQFTs and possible new representations for the Poincare group." Diss., Kansas State University, 2012. http://hdl.handle.net/2097/14139.

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Doctor of Philosophy
Department of Mathematics
Louis Crane
In this thesis we explore the possibilities of obtaining Topological Quantum Field Theories using cobordisms with corners to break further down in the structure of manifolds of a given dimension. The algebraic data obtained is described in the language of higher category theory, more precisely in its cubical approach which we explore here as well. Interesting connections are proposed to some important objects in Physics: the representations of the Poincaré group. Finally we will describe in great details the topological tools needed to describe the categories of cobordisms with corners and give some conjectures on their nature.

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Boixeda, Alvarez Pablo. "Affine Springer fibers and the representation theory of small quantum groups and related algebras." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/126920.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 125-128).
This thesis deals with the connections of Geometry and Representation Theory. In particular we study the representation theory of small quantum groups and Frobenius kernels and the geometry of an equivalued affine Springer fiber Fl[subscript ts] for s a regular semisimple element. In Chapter 2 we relate the center of the small quantum group with the cohomology of the above affine Springer fiber. This includes joint work with Bezrukavnikov, Shan and Vaserot. In Chapter 3 we study the geometry of the affine Springer fiber and in particular understand the fixed points of a torus action contained in each component. In Chapter 4 we further have a collection of algebraic results on the representation theory of Frobenius kernels. In particular we state some results pointing towards some construction of certain partial Verma functors and we compute this in the case of SL₂. We also compute the center of Frobenius kernels in the case of SL₂ and state a conjecture on a possible inductive construction of the general center.
by Pablo Boixeda Alvarez.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics

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Ho, Yanfang. "Group theoretical analysis of in-shell interaction in atoms." Scholarly Commons, 1985. https://scholarlycommons.pacific.edu/uop_etds/487.

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A group theoretic approach to Layzer's 1/2 expansion method is explored. In part this builds on earlier work of Wulfman(2), of Moshinsky et al(l4), and of Sinanoglu, Herrick(lS), and Kellman (16) on second row atoms. I investigate atoms with electrons in the 3s-3p-3d shell and find: 1. Wulfman's constant of motion accurately predicts configuration mixing for systems with two to eight electrons in the 3s-3p subshell. 2. The same constant of motion accurately predicts configuration mixing for systems with two electrons in the 3s-3p-3d shell. 3. It accurately predicts configuration mixing in systems of high angular momentum L and of high spin angular momentum S containing three electrons in the 3s-3p-3d shell, but gives less accurate results when L and S are both small. I also show how effective nuclear charges may be calculated by a group theoretical approach. In addition I explore several new methods for expressing electron repulsion operators in terms of operators of the 80(4,2) dynamical group of one - electron atoms.

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Xu, Guang-Hui. "Exploratory studies of group theoretic methods in atomic physics." Scholarly Commons, 1989. https://scholarlycommons.pacific.edu/uop_etds/2189.

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The properties of a physical system are determined by its equation of motion, and every such equation admits one-parameter groups which keep the equation invariant. Thus, for a particular system, if one can find the generator of a one-parameter group which keeps the equation and some further function or functional invariant, then one can change this system into others by changing the parameter, while keeping some properties constant. In this way, one can tell why different systems have some common properties. More importantly, one can use this method to find relationships between the physical properties of different systems. In the next section, we will illustrate the group theoretic approach by applying it to systems of two coupled oscillators and the hydrogen molecular ion. In section III of this thesis, we will investigate the helium atom system, considering both classical and quantum cases. In the quantum case our attention will be concentrated on the Schrodinger equation in matrix form. We will use a finite set of wavefunctions as our basis. Hence the results obtained will be approximate.

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Книги з теми "Quantum theory – Mathematics; Group theory"

Fröhlich, Jürg. Quantum groups, quantum categories, and quantum field theory. Berlin: Springer-Verlag, 1993.

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Noz, M. E. Special Relativity and Quantum Theory: A Collection of Papers on the Poincaré Group. Dordrecht: Springer Netherlands, 1988.

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author, Mertens Tom, and Veken, Frederik F. Van der, author, eds. Wilson lines in quantum field theory. Berlin: De Gruyter, 2014.

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Ryōshi jōhō e no hyōgenronteki apurōchi: Group representation approach to quantum information. Tōkyō-to Bunkyō-ku: Kyōritsu Shuppan, 2014.

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Kassel, Christian. Quantum Groups. New York, NY: Springer New York, 1995.

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Chari, Vyjayanthi. Guide to quantum groups. Cambridge: Cambridge University Press, 1995.

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Quantum field theory, conformal group theory, conformal field theory: Mathematical and conceptual foundations, physical and geometrical applications. Huntington, NY: Nova Science Publishers, 2001.

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Andrew, Pressley, ed. A guide to quantum groups. Cambridge: Cambridge University Press, 1994.

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Brundan, Jonathan. Quantum linear groups and representations of GLn(Fq). Providence, RI: American Mathematical Society, 2001.

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Franz, Uwe. Stochastic Processes and Operator Calculus on Quantum Groups. Dordrecht: Springer Netherlands, 1999.

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Частини книг з теми "Quantum theory – Mathematics; Group theory"

Fröhlich, Jürg, and Thomas Kerler. "Local quantum theory with braid group statistics." In Lecture Notes in Mathematics, 17–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0084246.

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Shirkov, Dmitrij V. "The Bogoliubov Renormalization Group in Theoretical and Mathematical Physics." In Quantum Field Theory, 157–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44482-3_10.

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Goldin, Gerald A., and David H. Sharp. "Diffeomorphism Group Representations in Relativistic Quantum Field Theory." In Trends in Mathematics, 47–56. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-01156-7_6.

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Hayashi, Masahito. "Mathematical Foundation for Quantum System." In Group Representation for Quantum Theory, 1–20. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44906-7_1.

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Drinfeld, V. G. "On some unsolved problems in quantum group theory." In Lecture Notes in Mathematics, 1–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0101175.

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Hook, Julian. "Chapter Nine. Some Musical Groups: Selected Applications of Group Theory in Music." In Diffusion, Quantum Theory, and Radically Elementary Mathematics, edited by William G. Faris, 209–28. Princeton: Princeton University Press, 2006. http://dx.doi.org/10.1515/9781400865253.209.

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Kimoto, Kazufumi. "Generalized Group–Subgroup Pair Graphs." In International Symposium on Mathematics, Quantum Theory, and Cryptography, 169–85. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_14.

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Abstract A regular finite graph is called a Ramanujan graph if its zeta function satisfies an analog of the Riemann Hypothesis. Such a graph has a small second eigenvalue so that it is used to construct cryptographic hash functions. Typically, explicit family of Ramanujan graphs are constructed by using Cayley graphs. In the paper, we introduce a generalization of Cayley graphs called generalized group–subgroup pair graphs, which are a generalization of group–subgroup pair graphs defined by Reyes-Bustos. We study basic properties, especially spectra of them.

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Voigt, Christian, and Robert Yuncken. "Representation Theory of Complex Semisimple Quantum Groups." In Lecture Notes in Mathematics, 287–356. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52463-0_6.

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Nuida, Koji. "Towards Constructing Fully Homomorphic Encryption without Ciphertext Noise from Group Theory." In International Symposium on Mathematics, Quantum Theory, and Cryptography, 57–78. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_8.

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Abstract In CRYPTO 2008, 1 year earlier than Gentry’s pioneering “bootstrapping” technique for the first fully homomorphic encryption (FHE) scheme, Ostrovsky and Skeith III had suggested a completely different approach towards achieving FHE. They showed that the $$\mathsf {NAND}$$ operator can be realized in some non-commutative groups; consequently, homomorphically encrypting the elements of the group will yield an FHE scheme, without ciphertext noise to be bootstrapped. However, no observations on how to homomorphically encrypt the group elements were presented in their paper, and there have been no follow-up studies in the literature. The aim of this paper is to exhibit more clearly what is sufficient and what seems to be effective for constructing FHE schemes based on their approach. First, we prove that it is sufficient to find a surjective homomorphism $$\pi :\widetilde{G} \rightarrow G$$ between finite groups for which bit operators are realized in G and the elements of the kernel of $$\pi $$ are indistinguishable from the general elements of $$\widetilde{G}$$. Secondly, we propose new methodologies to realize bit operators in some groups G. Thirdly, we give an observation that a naive approach using matrix groups would never yield secure FHE due to an attack utilizing the “linearity” of the construction. Then we propose an idea to avoid such “linearity” by using combinatorial group theory. Concretely realizing FHE schemes based on our proposed framework is left as a future research topic.

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Goldin, Gerald A. "Diffeomorphism Groups in Quantum Theory and Statistical Physics." In Trends in Mathematics, 345–50. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53305-2_23.

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Тези доповідей конференцій з теми "Quantum theory – Mathematics; Group theory"

Khots, Dmitriy, Boris Khots, Guillaume Adenier, Andrei Yu Khrennikov, Pekka Lahti, Vladimir I. Man'ko, and Theo M. Nieuwenhuizen. "Quantum Theory and Observer's Mathematics." In Quantum Theory. AIP, 2007. http://dx.doi.org/10.1063/1.2827314.

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SUDARSHAN, E. C. G. "GROUP THEORY OF DYNAMICAL MAPS." In Quantum Information and Computing. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774491_0026.

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Bender, Carl M., Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "PT-Symmetric Quantum Field Theory." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636813.

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Léandre, Rémi. "Large Deviations Estimates in Semi‐Group Theory." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990931.

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chen, jianhong. "Fundamental theorems from group theory." In 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), edited by Chi-Hua Chen, Xuexia Ye, and Hari Mohan Srivastava. SPIE, 2022. http://dx.doi.org/10.1117/12.2641075.

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Wu, Fengbo, Zijia Ye, Chengling Zhuge, and Jingyi Zou. "Classical results in group theory." In 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), edited by Chi-Hua Chen, Xuexia Ye, and Hari Mohan Srivastava. SPIE, 2022. http://dx.doi.org/10.1117/12.2639427.

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Wang, Yuancankun. "Fundamental results in group theory." In 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), edited by Chi-Hua Chen, Xuexia Ye, and Hari Mohan Srivastava. SPIE, 2022. http://dx.doi.org/10.1117/12.2639469.

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Bao, Zihui, Shiyang Hu, and Kecen Zhou. "Established results in group theory." In 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), edited by Chi-Hua Chen, Xuexia Ye, and Hari Mohan Srivastava. SPIE, 2022. http://dx.doi.org/10.1117/12.2639420.

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STERMAN, GEORGE. "PERTURBATIVE QUANTUM FIELD THEORY." In Proceedings of the International Conference on Fundamental Sciences: Mathematics and Theoretical Physics. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811264_0022.

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Braaten, Eric. "Renormalization group approach to thermal quantum field theory." In Computational quantum physics. AIP, 1992. http://dx.doi.org/10.1063/1.42603.

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Звіти організацій з теми "Quantum theory – Mathematics; Group theory"

Goldin, Gerald A., and David H. Sharp. Diffeomorphism Group Representations in Relativistic Quantum Field Theory. Office of Scientific and Technical Information (OSTI), December 2017. http://dx.doi.org/10.2172/1415360.

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Catterall, Simon, Roni Harnik, Veronika Hubeny, Christian Bauer, Asher Berlin, Zohreh Davoudi, Thomas Faulkner, et al. Report of the Snowmass 2021 Theory Frontier Topical Group on Quantum Information Science. Office of Scientific and Technical Information (OSTI), September 2022. http://dx.doi.org/10.2172/1892238.

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Hyman, J., W. Beyer, J. Louck, and N. Metropolis. Development of the applied mathematics originating from the group theory of physical and mathematical problems. Office of Scientific and Technical Information (OSTI), July 1996. http://dx.doi.org/10.2172/257450.

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Task A, High Energy Physics Program experiment and theory: Task B, High Energy Physics Program numerical simulation of quantum field theories. [Particle Physics Group, Physics Dept. , The Florida State Univ. , Tallahassee]. Office of Scientific and Technical Information (OSTI), January 1992. http://dx.doi.org/10.2172/6851536.

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