STOCHASTIC QUANTIZATION OF THE KINK SOLUTION OF ϕ4 FIELD THEORY

1989 ◽  
Vol 04 (01) ◽  
pp. 39-46
Author(s):  
RONALD KATES ◽  
ARNOLD ROSENBLUM
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Classical Field ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
Field Equations ◽  
Kink Solution

The method of Parisi-Wu Stochastic quantization in quantum field theory is compared to earlier work in classical field equations. The method is applied to solve for the propagator of ϕ4 field theory by perturbing the Kink solution.

scholarly journals NONLINEAR PHENOMENA IN CANONICAL STOCHASTIC QUANTIZATION

2008 ◽  
Vol 18 (09) ◽  
pp. 2787-2791
Author(s):  
HELMUTH HÜFFEL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Field Theories ◽  
Higgs Mechanism ◽  
Nonlinear Phenomena ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
Statistical System ◽  
Equilibrium Limit ◽  
Euclidean Quantum Field Theory

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochastic process. We discuss a novel formulation of the Higgs mechanism in QED.

scholarly journals The relation between quantum and classical field theory with a classical source

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200656
Author(s):  
S. A. Fulling ◽  
A. G. S. Landulfo ◽  
G. E. A. Matsas
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Classical Field Theory ◽  
Classical Field ◽  
Quantum Field ◽  
Schwarzschild Solution ◽  
Classical Source ◽  
Time Quantum ◽  
Perturbative Quantum ◽  
Classical Picture

Classical field theory is about fields and how they behave in space–time. Quantum field theory, in practice, usually seems to be about particles and how they scatter. Nevertheless, classical fields must emerge from quantum field theory in appropriate limits, and Michael Duff showed how this happens for the Schwarzschild solution in perturbative quantum gravity. In a series of papers, we and others have shown how classical radiation from an accelerated charge emerges from quantum field theory when the Unruh thermal effect is taken into account. Here, we sharpen those conclusions by showing that, even at finite times, the quantum picture is meaningful and is in close agreement with the classical picture.

scholarly journals A new approach to anomalous axial vector field theory – II

2021 ◽  
pp. 2150155
Author(s):  
A. K. Kapoor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vector Field ◽  
Axial Vector ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
New Approach ◽  
Four Dimensions

This work is continuation of a stochastic quantization program reported earlier. In this paper, we propose a consistent scheme of doing computations directly in four dimensions using conventional quantum field theory methods.

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.

Quantum field theory

1955 ◽  
Vol 231 (1186) ◽  
pp. 321-335 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Variational Principle ◽  
Schrodinger Equation ◽  
Classical Field Theory ◽  
Functional Expression ◽  
Scattering Matrix ◽  
Classical Field ◽  
Quantum Field ◽  
Relativistic Analogue

A functional expression resembling the scattering matrix is introduced into classical field theory, and with this foundation a postulate of quantization is introduced analogous to the definitions of Feynmann. From this are derived some alternative and more familiar forms of field theory. A variational principle is introduced which provides a relativistic analogue of the familiar non-relativistie variational principle for the Schrödinger equation.

SOLUTION OF A CLASS OF CONFORMAL QUANTUM FIELD THEORY MODELS IN D-DIMENSIONAL SPACE

1989 ◽  
Vol 04 (28) ◽  
pp. 2773-2790
Author(s):  
E.S. FRADKIN ◽  
M.Ya. PALCHIK
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Central Charge ◽  
Dimensional Space ◽  
Dimensional Euclidean Space ◽  
Constant Field ◽  
Quantum Field ◽  
Algebraic Equations ◽  
Field Equations ◽  
Parameter Symmetry

A method of solving a class of conformal quantum field theory models in D-dimensional Euclidean space-time is proposed. Some of the models are determined by regularized field equations. The method allows us to obtain closed differential equations for each Green function of fundamental and composite fields, and also algebraic equations for scale dimensions of fields. Each D>2-model involves an analogue of the central charge, i.e., a special scalar field P of dimension dP=D−2. When D=2, this becomes a constant field. We also obtain a new class of D=2 models with broken infinite parameter symmetry. Closed differential equation for Green functions of these models are found.

Lattice fractional quantum field theory: Exact differences approach

2020 ◽  
pp. 2140001
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Operators ◽  
Quantum Field ◽  
Field Equations ◽  
Fractional Quantum ◽  
Dimensional Spacetime ◽  
New Type ◽  
Unbounded Lattice ◽  
The Continuum

An approach, which is based on exact fractional differences, is used to formulate a lattice fractional field theories on unbounded lattice spacetime. An exact discretization of differential and integral operators of integer and non-integer orders is suggested. New type of fractional differences of integer and non-integer orders, which are represented by infinite series, are used in quantum field theory with non-locality. These exact differences have a property of universality, which means that these operators do not depend on the form of differential equations and the parameters of these equations. In addition, characteristic feature of the suggested differences is an implementation of the same algebraic properties that have the operator of differentiation (property of algebraic correspondence). Lattice analogs of the fractional-order N-dimensional differential operators are proposed. The continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum four-dimensional spacetime. The fractional field equations, which are derived from equations for lattice spacetime with long-range properties of power-law type, contain the Riesz type derivatives on non-integer orders with respect to spacetime coordinates.

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