Quantum field theory on a finite element: Self-coupled scalar field theory

1987 ◽  
Vol 289 ◽  
pp. 277-300 ◽  
Author(s):  
Toyoki Matsuyama
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Element ◽  
Scalar Field ◽  
Quantum Field ◽  
Scalar Field Theory

scholarly journals SHORT DISTANCE PROPERTIES FROM LARGE DISTANCE BEHAVIOR

1998 ◽  
Vol 13 (23) ◽  
pp. 4101-4122 ◽  
Author(s):  
PAUL MANSFIELD ◽  
MARCOS SAMPAIO ◽  
JIANNIS PACHOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Large Distance ◽  
Short Distance ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
Expansion Coefficients ◽  
Distance Behavior ◽  
Distance Properties

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficients can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counterterms. We also describe an approximate simplification that occurs for the sine–Gordon and sinh–Gordon vacuum functionals.

scholarly journals Renormalization in open quantum field theory. Part I. Scalar field theory

2017 ◽  
Vol 2017 (11) ◽  
Author(s):  
Avinash Baidya ◽  
Chandan Jana ◽  
R. Loganayagam ◽  
Arnab Rudra
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
Open Quantum

scholarly journals Chaotic instantons in scalar field theory

2017 ◽  
Vol 14 (10) ◽  
pp. 1750135
Author(s):  
Andrea Addazi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Quantum Tunneling ◽  
Enhancement Factor ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
New Class ◽  
Source Field ◽  
True Vacuum

We consider a new class of instantons in context of quantum field theory of a scalar field coupled with a chaotic background source field. We show how the instanton associated to the quantum tunneling from a metastable false to the true vacuum will be corrected by an exponential enhancement factor. Possible implications are discussed.

scholarly journals QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

1999 ◽  
Vol 11 (05) ◽  
pp. 519-532 ◽  
Author(s):  
SEBASTIANO CARPI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Scaling Limit ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Complex Scalar

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

scholarly journals THE BOLTZMANN EQUATION IN SCALAR FIELD THEORY

1998 ◽  
Vol 13 (24) ◽  
pp. 4281-4288 ◽  
Author(s):  
F. T. BRANDT ◽  
J. FRENKEL ◽  
A. GUERRA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Temperature Limit ◽  
Equation Of Motion ◽  
Green Functions ◽  
Static Case ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
High Temperature Limit ◽  
Classical Transport

We derive the classical transport equation, in scalar field theory with a g2V(ϕ) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action Γ which generates all the n-point Green functions in the high-temperature limit. An explicit and closed form is given for Γ in the static case.

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.

Metastable vacua in quantum field theory (QFT)

2021 ◽  
pp. 919-941
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Imaginary Part ◽  
Classical Limit ◽  
Three Dimensions ◽  
Quantum Field ◽  
Field Equations ◽  
Barrier Penetration ◽  
General Scalar

The methods to evaluate barrier penetration effects, in the semi-classical limit are generalized to quantum field theory (QFT). Since barrier penetration is associated with classical motion in imaginary time, the QFT is considered in its Euclidean formulation. In the representation of QFT in terms of field integrals, in the semi-classical limit, barrier penetration is related to finite action solutions (instantons) of the classical field equations. The evaluation of instanton contributions at leading order is explained, the main new problem arising from ultraviolet divergences. The lifetime of metastable states is related to the imaginary part of the ‘ground state’ energy. However, for later purpose, it is useful to calculate the imaginary part not only of the vacuum amplitude, but also of correlation functions. In the case of the vacuum amplitude, the instanton contribution is proportional to the space–time volume. Therefore, dividing by the volume, one obtains the probability per unit time and unit volume of a metastable pseudo-vacuum to decay. A scalar field theory with a φ4 interaction, generalization of the quartic anharmonic oscillator is discussed in two and three dimensions, dimensions in which the theory is super-renormalizable, then more general scalar field theories are considered.

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