scholarly journals The Casimir effect in string theory

2019 ◽  
Vol 34 (09) ◽  
pp. 1950049
Author(s):  
Alexandros Kehagias ◽  
Hervé Partouche
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
String Theory ◽  
Casimir Effect ◽  
Quantum Field ◽  
Parallel Plates ◽  
Projection Formula ◽  
Conducting Material ◽  
Modular Invariant ◽  
Heterotic String Theory

We discuss the Casimir effect in heterotic string theory. This is done by considering a [Formula: see text] twist acting on one external compact direction and three internal coordinates. The hyperplanes fixed by the orbifold generator [Formula: see text] realize the two infinite parallel plates. For the latter to behave as “conducting material,” we implement in a modular invariant way the projection [Formula: see text] on the spectrum running in the vacuum-to-vacuum amplitude at one-loop. Hence, the relevant projector to account for the Casimir effect is orthogonal to that commonly used in string orbifold models which is [Formula: see text]. We find that this setup yields the same net force acting on the plates in the context of quantum field theory and string theory. However, when supersymmetry is not present from the onset, finiteness of the resultant force in field theory is reached by adding formally infinite forces acting on either side of each plate, while in string theory, both contributions are finite. On the contrary, when supersymmetry is spontaneously broken à la Scherk–Schwarz, finiteness of each contribution is fulfilled in field and string theory.

scholarly journals Perturbative Versus Non-Perturbative Quantum Field Theory: Tao’s Method, the Casimir Effect, and Interacting Wightman Theories

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 229
Author(s):  
Walter Felipe Wreszinski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Casimir Effect ◽  
Asymptotic Series ◽  
Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
Parallel Plates ◽  
Perturbative Approach ◽  
Usual Theory

We dwell upon certain points concerning the meaning of quantum field theory: the problems with the perturbative approach, and the question raised by ’t Hooft of the existence of the theory in a well-defined (rigorous) mathematical sense, as well as some of the few existent mathematically precise results on fully quantized field theories. Emphasis is brought on how the mathematical contributions help to elucidate or illuminate certain conceptual aspects of the theory when applied to real physical phenomena, in particular, the singular nature of quantum fields. In a first part, we present a comprehensive review of divergent versus asymptotic series, with qed as background example, as well as a method due to Terence Tao which conveys mathematical sense to divergent series. In a second part, we apply Tao’s method to the Casimir effect in its simplest form, consisting of perfectly conducting parallel plates, arguing that the usual theory, which makes use of the Euler-MacLaurin formula, still contains a residual infinity, which is eliminated in our approach. In the third part, we revisit the general theory of nonperturbative quantum fields, in the form of newly proposed (with Christian Jaekel) Wightman axioms for interacting field theories, with applications to “dressed” electrons in a theory with massless particles (such as qed), as well as unstable particles. Various problems (mostly open) are finally discussed in connection with concrete models.

scholarly journals ON THE QUANTUM THEORY OF MASSLESS SPIN-3/2 FIELD IN MINKOWSKI SPACETIME

2006 ◽  
Vol 03 (07) ◽  
pp. 1303-1312 ◽  
Author(s):  
WEIGANG QIU ◽  
FEI SUN ◽  
HONGBAO ZHANG
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Casimir Effect ◽  
Minkowski Spacetime ◽  
Quantum Field ◽  
Explicit Result ◽  
Massless Spin ◽  
The Many ◽  
The One

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the many-particle's quantum field theory. The explicit result presented here is useful for the investigation of spin-3/2 field in various circumstances such as supergravity, twistor programme, Casimir effect, and quantum inequality.

scholarly journals Advances in String Theory in Curved Backgrounds: A Synthesis Report

2003 ◽  
Vol 18 (12) ◽  
pp. 2011-2022 ◽  
Author(s):  
N. G. Sanchez
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
String Theory ◽  
Quantum Field ◽  
De Sitter ◽  
Conformal Field ◽  
Dual Relation ◽  
New Feature ◽  
Synthesis Report ◽  
Gravitational Wave Background

A synthetic report of the advances in the study of classical and quantum string dynamics in curved backgrounds is provided, namely : the new feature of Multistring solutions; the mass spectrum of Strings in Curved backgrounds; The effect of a Cosmological Constant and of Spacial Curvature on Classical and Quantum Strings; Classical splitting of Fundamental Strings; The General String Evolution in constant Curvature Spacetimes; The Conformal Invariance Effects; Strings on plane fronted and gravitational shock waves, string falling on spacetime singularities and its spectrum. New Developments in String Gravity and String Cosmology are reported: String driven cosmology and its Predictions; The primordial gravitational wave background; Non-singular string cosmologies from Exact Conformal Field Theories; Quantum Field Theory, String Temperature and the String Phase of de Sitter space-time; Hawking Radiation in String Theory and the String Phase of Black Holes; New Dual Relation between Quantum Field Theory regime and String regime and the "QFT/String Tango"; New Coherent String States and Minimal Uncertainty Principle in string theory.

scholarly journals Galilean covariance, Casimir effect and Stefan–Boltzmann law at finite temperature

2017 ◽  
Vol 32 (16) ◽  
pp. 1750094 ◽  
Author(s):  
S. C. Ulhoa ◽  
A. F. Santos ◽  
Faqir C. Khanna
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Temperature ◽  
Temperature Effects ◽  
Casimir Effect ◽  
Quantum Field ◽  
Covariant Quantum ◽  
Thermo Field Dynamics ◽  
Boltzmann Law ◽  
Galilean Covariance

The Galilean covariance, formulated in 5-dimensions space, describes the nonrelativistic physics in a way similar to a Lorentz covariant quantum field theory being considered for relativistic physics. Using a nonrelativistic approach the Stefan–Boltzmann law and the Casimir effect at finite temperature for a particle with spin zero and 1/2 are calculated. The thermo field dynamics is used to include the finite temperature effects.

scholarly journals Duality in quantum field theory (and string theory)

1998 ◽  
Author(s):  
Luis Álvarez-Gaumé ◽  
Frederic Zamora
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
String Theory ◽  
Quantum Field

REGULARIZATION OF GENERAL MULTIDIMENSIONAL EPSTEIN ZETA-FUNCTIONS

1989 ◽  
Vol 01 (01) ◽  
pp. 113-128 ◽  
Author(s):  
E. ELIZALDE ◽  
A. ROMEO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Partition Function ◽  
Zeta Function ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Zeta Functions ◽  
Quantum Field ◽  
Type Formula

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.

scholarly journals A NONASSOCIATIVE QUATERNION SCALAR FIELD THEORY

2013 ◽  
Vol 28 (35) ◽  
pp. 1350163 ◽  
Author(s):  
SERGIO GIARDINO ◽  
PAULO TEOTÔNIO-SOBRINHO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
String Theory ◽  
Hopf Algebra ◽  
Scalar Product ◽  
Quantum Field ◽  
Quantum Algebras ◽  
Function Algebras ◽  
Nonlinear Quantum

A nonassociative Groenewold–Moyal (GM) plane is constructed using quaternion-valued function algebras. The symmetrized multiparticle states, the scalar product, the annihilation/creation algebra and the formulation in terms of a Hopf algebra are also developed. Nonassociative quantum algebras in terms of position and momentum operators are given as the simplest examples of a framework whose applications may involve string theory and nonlinear quantum field theory.

scholarly journals Duality in Quantum Field Theory (and String Theory)

1998 ◽  
Author(s):  
Luis Álvarez-Gaumé ◽  
Frederic Zamora
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
String Theory ◽  
Quantum Field
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