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Journal articles on the topic 'Zeta regularization'

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Published: 9 March 2023
Last updated: 11 March 2023

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1

Lavrov, P. M. "Generalized zeta-function regularization." Soviet Physics Journal 30, no. 5 (May 1987): 359–62. http://dx.doi.org/10.1007/bf00900080.

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2

Allouche, Jean-Paul. "Zeta-regularization of arithmetic sequences." EPJ Web of Conferences 244 (2020): 01008. http://dx.doi.org/10.1051/epjconf/202024401008.

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Is it possible to give a reasonable value to the infinite product 1 × 2 × 3 × · · · × n × · · · ? In other words, can we define some sort of convergence of the finite product 1 × 2 × 3 × · · · × n when n goes to infinity? One way is to relate this product to the R√iemann zeta function and to its analytic continuation. This approach leads to: 1 × 2 × 3 × · · · × n × · · · = 2π. More generally the “zeta-regularization” of an infinite product consists of introducing a related Dirichlet series and its analytic continuation at 0 (if it exists). We will survey some properties of this generalized product and allude to applications. Then we will give two families of possibly new examples: one unifies and generalizes known results for the zeta-regularization of the products of Fibonacci, balanced and Lucas-balanced numbers; the other studies the zeta-regularized products of values of classical arithmetic functions. Finally we ask for a possible zeta-regularity notion of complexity.
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3

AKIRA, ASADA. "REGULARIZED CALCULUS: AN APPLICATION OF ZETA REGULARIZATION TO INFINITE DIMENSIONAL GEOMETRY AND ANALYSIS." International Journal of Geometric Methods in Modern Physics 01, no. 01n02 (April 2004): 107–57. http://dx.doi.org/10.1142/s0219887804000071.

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A method of regularization in infinite dimensional calculus, based on spectral zeta function and zeta regularization is proposed. As applications, a mathematical justification of appearance of Ray–Singer determinant in Gaussian Path integral, regularized volume form of the sphere of a Hilbert space with the determinant bundle, eigenvalue problems of regularized Laplacian, are investigated. Geometric counterparts of regularization procedure are also discussed applying arguments from noncommutative geometry.
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4

Reuter, M. "Chiral anomalies and zeta-function regularization." Physical Review D 31, no. 6 (March 15, 1985): 1374–85. http://dx.doi.org/10.1103/physrevd.31.1374.

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5

ELIZALDE, E., and A. ROMEO. "REGULARIZATION OF GENERAL MULTIDIMENSIONAL EPSTEIN ZETA-FUNCTIONS." Reviews in Mathematical Physics 01, no. 01 (January 1989): 113–28. http://dx.doi.org/10.1142/s0129055x89000055.

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We study expressions for the regularization of general multidimensional Epstein zeta-functions of the type [Formula: see text] After reviewing some classical results in the light of the extended proof of zeta-function regularization recently obtained by the authors, approximate but very quickly convergent expressions for these functions are derived. This type of analysis has many interesting applications, e.g. in any quantum field theory defined in a partially compactified Euclidean spacetime or at finite temperature. As an example, we obtain the partition function for the Casimir effect at finite temperature.
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6

Fermi, Davide, and Livio Pizzocchero. "Local Zeta Regularization and the Casimir Effect." Progress of Theoretical Physics 126, no. 3 (September 2011): 419–34. http://dx.doi.org/10.1143/ptp.126.419.

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7

Shiekh, A. Y. "Zeta-function regularization of quantum field theory." Canadian Journal of Physics 68, no. 7-8 (July 1, 1990): 620–29. http://dx.doi.org/10.1139/p90-093.

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Analytic continuation leads to the finite renormalization of a quantum field theory. This is illustrated in a determination of the two loop renormalization group functions for [Formula: see text] in four dimensions.
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8

Shiekh, A. Y. "Operator regularization of Feynman diagrams at multiloop order." Canadian Journal of Physics 89, no. 11 (November 2011): 1149–54. http://dx.doi.org/10.1139/p11-110.

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It has been previously believed not possible to use operator regularization with Feynman diagrams, but such an option would greatly simplify matters, as operator regularization is otherwise limited to the more complicated Schwinger approach. Further, operator regularization, unlike zeta function regularization, is not limited to one-loop order, and preserves supersymmetry, unlike dimensional regularization. In this work, we investigate operator regularization at the more probing two-loop order, and find not only compatibility but that the simplification associated with Feynman diagrams is retained.
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9

ZHAI, XIANG-HUA, YANG YANG, and JIE LAI. "FINITE TEMPERATURE CASIMIR EFFECT FOR PERFECTLY CONDUCTING PARALLEL PLATES IN (D + 1)-DIMENSIONAL SPACETIME." International Journal of Modern Physics: Conference Series 07 (January 2012): 202–8. http://dx.doi.org/10.1142/s2010194512004278.

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We study the finite temperature Casimir effect between perfectly conducting parallel plates in (D + 1)-dimensional spacetime by using zeta-function regularization technique. We get the analytical results for Casimir energy, Casimir free energy, Casimir entropy and Casimir pressure expressed by Riemann zeta function and Bessel function and give the asymptotic expressions for low and high temperature limits. In the case of D = 3, through mathematic transformation, we reproduce the standard results in the literature which is in most times obtained by using Green's function regularization technique.
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10

Lin, Rui-Hui, and Xiang-Hua Zhai. "Equivalence of zeta function technique and Abel–Plana formula in regularizing the Casimir energy of hyper-rectangular cavities." Modern Physics Letters A 29, no. 35 (November 17, 2014): 1450181. http://dx.doi.org/10.1142/s0217732314501818.

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Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic continuation. By contrast, Abel–Plana formula method permits explicit separation of divergent terms. In regularizing the Casimir energy for a massless scalar field in a D-dimensional rectangular box, we give the rigorous proof of the equivalence of the two methods by deriving the reflection formula of Epstein zeta function from repeatedly application of Abel–Plana formula and giving the physical interpretation of the infinite integrals. Our study may help with the confidence of choosing any regularization method at convenience among the frequently used ones, especially the zeta function method, without the doubts of physical meanings or mathematical consistency.
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11

ELIZALDE, EMILIO. "ZETA FUNCTION REGULARIZATION IN CASIMIR EFFECT CALCULATIONS AND J. S. DOWKER'S CONTRIBUTION." International Journal of Modern Physics: Conference Series 14 (January 2012): 57–72. http://dx.doi.org/10.1142/s2010194512007234.

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A summary of relevant contributions, ordered in time, to the subject of operator zeta functions and their application to physical issues is provided. The description ends with the seminal contributions of Stephen Hawking and Stuart Dowker and collaborators, considered by many authors as the actual starting point of the introduction of zeta function regularization methods in theoretical physics, in particular, for quantum vacuum fluctuation and Casimir effect calculations. After recalling a number of the strengths of this powerful and elegant method, some of its limitations are discussed. Finally, recent results of the so called operator regularization procedure are presented.
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12

ELIZALDE, EMILIO. "ZETA FUNCTION REGULARIZATION IN CASIMIR EFFECT CALCULATIONS AND J. S. DOWKER's CONTRIBUTION." International Journal of Modern Physics A 27, no. 15 (June 14, 2012): 1260005. http://dx.doi.org/10.1142/s0217751x12600056.

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A summary of relevant contributions, ordered in time, to the subject of operator zeta functions and their application to physical issues is provided. The description ends with the seminal contributions of Stephen Hawking and Stuart Dowker and collaborators, considered by many authors as the actual starting point of the introduction of zeta function regularization methods in theoretical physics, in particular, for quantum vacuum fluctuation and Casimir effect calculations. After recalling a number of the strengths of this powerful and elegant method, some of its limitations are discussed. Finally, recent results of the so-called operator regularization procedure are presented.
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13

Li, Zhong-hua. "Higher order shuffle regularization for multiple zeta values." Proceedings of the American Mathematical Society 138, no. 07 (July 1, 2010): 2321. http://dx.doi.org/10.1090/s0002-9939-10-10354-2.

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14

Elizalde, E. "Zeta-function regularization is uniquely defined and well." Journal of Physics A: Mathematical and General 27, no. 9 (May 7, 1994): L299—L304. http://dx.doi.org/10.1088/0305-4470/27/9/010.

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15

Menotti, Pietro. "Noninvariant zeta-function regularization in quantum Liouville theory." Physics Letters B 650, no. 5-6 (July 2007): 432–39. http://dx.doi.org/10.1016/j.physletb.2007.05.053.

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16

Elizalde, E., and A. Romeo. "Rigorous extension of the proof of zeta-function regularization." Physical Review D 40, no. 2 (July 15, 1989): 436–43. http://dx.doi.org/10.1103/physrevd.40.436.

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17

Wospakrik, Hans J. "Nonrecursive zeta-function regularization of the Fujikawa anomaly factor." Physical Review D 40, no. 4 (August 15, 1989): 1367–69. http://dx.doi.org/10.1103/physrevd.40.1367.

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18

Weldon, H. A. "Proof of zeta-function regularization of high-temperature expansions." Nuclear Physics B 270 (January 1986): 79–91. http://dx.doi.org/10.1016/0550-3213(86)90545-6.

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19

Actor, Alfred. "More on Zeta-Function Regularization of High-Temperature Expansions." Fortschritte der Physik/Progress of Physics 35, no. 12 (1987): 793–829. http://dx.doi.org/10.1002/prop.2190351202.

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20

HADASZ, LESZEK. "GROUND STATE ENERGY OF THE MODIFIED NAMBU–GOTO STRING." Modern Physics Letters A 13, no. 08 (March 14, 1998): 605–14. http://dx.doi.org/10.1142/s0217732398000656.

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We calculate, using zeta function regularization method, semiclassical energy of the Nambu–Goto string supplemented with the boundary, Gauss–Bonnet term in the action and discuss the tachyonic ground state problem.
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21

Fabiano, Nikola. "Zeta function and some of its properties." Vojnotehnicki glasnik 68, no. 4 (2020): 895–906. http://dx.doi.org/10.5937/vojtehg68-28535.

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Introduction/purpose: Some properties of the zeta function will be shown as well as its applications in calculus, in particular the "golden nugget formula" for the value of the infinite sum 1 + 2 + 3 + · · · . Some applications in physics will also be mentioned. Methods: Complex plane integrations and properties of the Gamma function will be used from the definition of the function to its analytic extension. Results: From the original definition of the z(s) function valid for s > 1 a meromorphic function is obtained on the whole complex plane with a simple pole in s = 1. Conclusion: The relevance of the zeta function cannot be overstated, ranging from the infinite series to the number theory, regularization in theoretical physics, the Casimir force, and many other fields.
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22

LOHIYA, DAKSH. "COMMON ANALYTIC BASIS OF THE ζ-FUNCTION AND THE DIMENSIONAL REGULARIZATION SCHEMES." Modern Physics Letters A 04, no. 09 (May 10, 1989): 863–67. http://dx.doi.org/10.1142/s0217732389001015.

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The analytic continuation invoked in the theory of generalized zeta functions associated with infinite-dimensional operators is shown to be equivalent in structure to the basic analytic methods deployed in dimensional regularization.
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23

Elizalde, Emilio. "Zeta Functions and the Cosmos—A Basic Brief Review." Universe 7, no. 1 (December 30, 2020): 5. http://dx.doi.org/10.3390/universe7010005.

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This is a very basic and pedagogical review of the concepts of zeta function and of the associated zeta regularization method, starting from the notions of harmonic series and of divergent sums in general. By way of very simple examples, it is shown how these powerful methods are used for the regularization of physical quantities, such as quantum vacuum fluctuations in various contexts. In special, in Casimir effect setups, with a note on the dynamical Casimir effect, and mainly concerning its application in quantum theories in curved spaces, subsequently used in gravity theories and cosmology. The second part of this work starts with an essential introduction to large scale cosmology, in search of the observational foundations of the Friedmann-Lemaître-Robertson-Walker (FLRW) model, and the cosmological constant issue, with the very hard problems associated with it. In short, a concise summary of all these interrelated subjects and applications, involving zeta functions and the cosmos, and an updated list of the pioneering and more influential works (according to Google Scholar citation counts) published on all these matters to date, are provided.
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24

ALVES, M. S., and J. BARCELOS-NETO. "TRACE ANOMALY IN A THEORY WITH BOSONS AND FERMIONS." Modern Physics Letters A 05, no. 16 (July 10, 1990): 1291–98. http://dx.doi.org/10.1142/s0217732390001463.

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We study the trace anomaly in a theory involving bosons and fermions which has supersymmetry as a particular case. We use the path integral formalism and the zeta function as the regularization method.
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25

Escalante, F. "Zeta function regularization technique in the electrostatics context for discrete charge distributions." European Journal of Physics 43, no. 3 (April 5, 2022): 035810. http://dx.doi.org/10.1088/1361-6404/ac5915.

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Abstract Spectral functions, such as the zeta functions, are widely used in quantum field theory to calculate physical quantities. In this work, we compute the electrostatic potential and field due to an infinite discrete distribution of point charges, using the zeta function regularization technique. This method allows us to remove the infinities that appear in the resulting expression. We found that the asymptotic behavior dependence of the potential and field is similar to the cases of continuous charge distribution. Finally, this exercise can be useful for graduate students to explore spectral and special functions.
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26

BYTSENKO, A. A., A. E. GONÇALVES, and S. ZERBINI. "ONE-LOOP EFFECTIVE POTENTIAL FOR SCALAR AND VECTOR FIELDS ON HIGHER-DIMENSIONAL NONCOMMUTATIVE FLAT MANIFOLDS." Modern Physics Letters A 16, no. 23 (July 30, 2001): 1479–86. http://dx.doi.org/10.1142/s0217732301004765.

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The non-planar contribution to the effective potentials for massless scalar and vector quantum field theories on D-dimensional manifold with p compact noncommutative extra dimensions is evaluated by means of dimensional regularization implemented by zeta function techniques. It is found that, the zeta function associated with the one-loop operator may not be regular at the origin. Thus, the related heat kernel trace has a logarithmic term in the short t asymptotic expansion. Consequences of this fact are briefly discussed.
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27

Hirose, Minoru, Hideki Murahara, and Shingo Saito. "Polynomial Generalization of the Regularization Theorem for Multiple Zeta Values." Publications of the Research Institute for Mathematical Sciences 56, no. 1 (January 21, 2020): 207–15. http://dx.doi.org/10.4171/prims/56-1-9.

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28

Fujimoto, Minoru, and Kunihiko Uehara. "The Regularization for the Zeta Functions with Physical Applications II." International Journal of Theoretical and Mathematical Physics 2, no. 5 (December 1, 2012): 130–35. http://dx.doi.org/10.5923/j.ijtmp.20120205.06.

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29

Reuter, M., and W. Dittrich. "Anomalies in odd-dimensional space-times and zeta-function regularization." Physical Review D 33, no. 2 (January 15, 1986): 601–4. http://dx.doi.org/10.1103/physrevd.33.601.

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30

Chodos, Alan, and András Kaiser. "Zeta function regularization in de Sitter space: The Minkowski limit." Journal of Mathematical Physics 38, no. 9 (September 1997): 4771–82. http://dx.doi.org/10.1063/1.532122.

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31

Elizalde, Emilio, Luciano Vanzo, and Sergio Zerbini. "Zeta-Function Regularization, the Multiplicative Anomaly and the Wodzicki Residue." Communications in Mathematical Physics 194, no. 3 (June 1, 1998): 613–30. http://dx.doi.org/10.1007/s002200050371.

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32

Schakel, A. M. J. "Zeta function regularization of infrared divergences in Bose-Einstein condensation." Journal of Physical Studies 7, no. 2 (2003): 140–55. http://dx.doi.org/10.30970/jps.07.140.

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33

Actor, Alfred. "Zeta function regularization of high-temperature expansions in field theory." Nuclear Physics B 265, no. 4 (April 1986): 689–719. http://dx.doi.org/10.1016/0550-3213(86)90336-6.

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34

Vanzo, Luciano, and Sergio Zerbini. "Critical dimension of bosonic string theory and zeta-function regularization." Physics Letters B 214, no. 1 (November 1988): 51–54. http://dx.doi.org/10.1016/0370-2693(88)90450-9.

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35

Fermi, Davide, and Livio Pizzocchero. "Local zeta regularization and the scalar Casimir effect III. The case with a background harmonic potential." International Journal of Modern Physics A 30, no. 35 (December 20, 2015): 1550213. http://dx.doi.org/10.1142/s0217751x15502139.

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Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we renormalize the vacuum expectation value of the stress-energy tensor (and of the total energy) for a scalar field in presence of an external harmonic potential.
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36

COGNOLA, GUIDO, and SERGIO ZERBINI. "SOME PHYSICAL APPLICATIONS OF THE HEAT KERNEL EXPANSION." Modern Physics Letters A 03, no. 06 (May 1988): 599–605. http://dx.doi.org/10.1142/s0217732388000714.

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A systematic analysis of anomalies, for Dirac fermions in external gravitational fields with nonvanishing torsion, is performed using a method based on Euclidean path integral, zeta function regularization and heat kernel expansion. Many known results are recovered and some new ones have been found.
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37

Fermi, Davide, and Livio Pizzocchero. "Local zeta regularization and the scalar Casimir effect IV: The case of a rectangular box." International Journal of Modern Physics A 31, no. 04n05 (February 3, 2016): 1650003. http://dx.doi.org/10.1142/s0217751x16500032.

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Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we compute the renormalized vacuum expectation value of several observables (in particular, of the stress–energy tensor) for a massless scalar field confined within a rectangular box of arbitrary dimension.
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38

Erdas, Andrea, and Kevin P. Seltzer. "Finite temperature Casimir effect for massive scalars in a magnetic field." International Journal of Modern Physics A 29, no. 17 (June 26, 2014): 1450091. http://dx.doi.org/10.1142/s0217751x14500912.

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The finite temperature Casimir effect for a charged, massive scalar field confined between very large, perfectly conducting parallel plates is studied using the zeta function regularization technique. The scalar field satisfies Dirichlet boundary conditions at the plates and a magnetic field perpendicular to the plates is present. Four equivalent expressions for the zeta function are obtained, which are exact to all orders in the magnetic field strength, temperature, scalar field mass and plate distance. The zeta function is used to calculate the Helmholtz free energy of the scalar field and the Casimir pressure on the plates, in the case of high temperature, small plate distance, strong magnetic field and large scalar mass. In all cases, simple analytic expressions of the zeta function, free energy and pressure are obtained, which are very accurate and valid for practically all values of temperature, plate distance, magnetic field and mass.
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39

Kaneko, Masanobu, Ce Xu, and Shuji Yamamoto. "A generalized regularization theorem and Kawashima's relation for multiple zeta values." Journal of Algebra 580 (August 2021): 247–63. http://dx.doi.org/10.1016/j.jalgebra.2021.04.005.

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40

Bilal, Adel, and Frank Ferrari. "Multi-loop zeta function regularization and spectral cutoff in curved spacetime." Nuclear Physics B 877, no. 3 (December 2013): 956–1027. http://dx.doi.org/10.1016/j.nuclphysb.2013.10.003.

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41

Ortenzi, G., and M. Spreafico. "Zeta function regularization for a scalar field in a compact domain." Journal of Physics A: Mathematical and General 37, no. 47 (November 11, 2004): 11499–517. http://dx.doi.org/10.1088/0305-4470/37/47/018.

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42

Bocardo-Gaspar, Miriam, H. García-Compeán, and W. A. Zúñiga-Galindo. "Regularization of p-adic string amplitudes, and multivariate local zeta functions." Letters in Mathematical Physics 109, no. 5 (November 23, 2018): 1167–204. http://dx.doi.org/10.1007/s11005-018-1137-1.

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43

Lavrov, P. M. "Regularization using the generalized zeta function in the proper-time method." Soviet Physics Journal 30, no. 11 (November 1987): 972–76. http://dx.doi.org/10.1007/bf00898522.

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44

Fermi, Davide. "The Casimir energy anomaly for a point interaction." Modern Physics Letters A 35, no. 03 (January 16, 2020): 2040008. http://dx.doi.org/10.1142/s0217732320400088.

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The Casimir energy for a massless, neutral scalar field in presence of a point interaction is analyzed using a general zeta-regularization approach developed in earlier works. In addition to a regular bulk contribution, there arises an anomalous boundary term which is infinite despite renormalization. The intrinsic nature of this anomaly is briefly discussed.
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45

COGNOLA, GUIDO, and LUCIANO VANZO. "THERMODYNAMIC POTENTIAL FOR SCALAR FIELDS IN SPACE-TIME WITH HYPERBOLIC SPATIAL PART." Modern Physics Letters A 07, no. 39 (December 21, 1992): 3677–88. http://dx.doi.org/10.1142/s0217732392003104.

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The thermodynamic potential for a charged scalar field of mass m on a (3+1)-dimensional space-time with hyperbolic H3/Γ spatial part is evaluated using zeta-function and heat kernel regularization techniques and Selberg trace formula for co-compact group Γ. High and low temperature expansions are obtained and discussed in detail.
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46

JALALZADEH, S., and F. DARABI. "ONE-LOOP QUANTUM COSMOLOGICAL CORRECTION TO THE GRAVITATIONAL CONSTANT IN THE CLOSED FRIEDMANN–ROBERTSON–WALKER UNIVERSE." International Journal of Modern Physics A 25, no. 21 (August 20, 2010): 4111–22. http://dx.doi.org/10.1142/s0217751x10050275.

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In this paper, we calculate the one-loop quantum cosmological corrections to the kink energy in the closed Friedmann–Robertson–Walker universe in which the fluctuation potential V″ has a shape invariance property. We use the generalized zeta-function regularization method to implement our setup for describing quantum kink-like states. It is conjectured that the corrections lead to the renormalized gravitational constant.
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47

Voros, André. "Zeta-regularization for exact-WKB resolution of a general 1D Schrödinger equation." Journal of Physics A: Mathematical and Theoretical 45, no. 37 (September 4, 2012): 374007. http://dx.doi.org/10.1088/1751-8113/45/37/374007.

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48

Furusho, Hidekazu, and Amir Jafari. "Regularization and generalized double shuffle relations for $p$-adic multiple zeta values." Compositio Mathematica 143, no. 05 (September 2007): 1089–107. http://dx.doi.org/10.1112/s0010437x0600265x.

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49

Kamath, S. G. "Zeta-Function Regularization and Scale and Conformal Anomalies for the Landau Problem." Modern Physics Letters A 12, no. 34 (November 10, 1997): 2631–40. http://dx.doi.org/10.1142/s0217732397002764.

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The technique of ζ-function regularization is used to calculate the anomalies associated with the transformations (t→ e-ρt) and (1/t → 1/t - a) for the Landau Lagrangian. The proper-time transformation function Kij(t,τ;t′,0) now needs to be evaluated exactly, thereby leading to an exact ζ(s,t) for the Landau problem. As a generalization, the calculation when extended to the non-relativistic |ϕ|4 theory in 2+1 dimensions leads to difficulties. We shall discuss some of the difficulties in detail.
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50

Elizalde, Emilio, Sergei D. Odintsov, and August Romeo. "Zeta‐regularization of the O(N) nonlinear sigma model in D dimensions." Journal of Mathematical Physics 37, no. 3 (March 1996): 1128–47. http://dx.doi.org/10.1063/1.531437.

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