Solution of quantum field equations

1987 ◽  
pp. 462-465
Author(s):  
Izrail Moiseevich Gelfand
Keyword(s):  
Quantum Field ◽  
Field Equations

scholarly journals THE MASTER WARD IDENTITY

2002 ◽  
Vol 14 (09) ◽  
pp. 977-1049 ◽  
Author(s):  
M. DÜTSCH ◽  
F.-M. BOAS
Keyword(s):  
Ward Identity ◽  
Brst Symmetry ◽  
Quantum Field ◽  
Field Equations ◽  
Normalization Condition ◽  
Abelian Gauge ◽  
Algebra Of Observables ◽  
Local Construction ◽  
Perturbative Quantum ◽  
Equal Time Commutation

In the framework of perturbative quantum field theory (QFT) we propose a new, universal (re)normalization condition (called 'master Ward identity') which expresses the symmetries of the underlying classical theory. It implies for example the field equations, energy-momentum, charge- and ghost-number conservation, renormalized equal-time commutation relations and BRST-symmetry. It seems that the master Ward identity can nearly always be satisfied, the only exceptions we know are the usual anomalies. We prove the compatibility of the master Ward identity with the other (re)normalization conditions of causal perturbation theory, and for pure massive theories we show that the 'central solution' of Epstein and Glaser fulfills the master Ward identity, if the UV-scaling behavior of its individual terms is not relatively lowered. Application of the master Ward identity to the BRST-current of non-Abelian gauge theories generates an identity (called 'master BRST-identity') which contains the information which is needed for a local construction of the algebra of observables, i.e. the elimination of the unphysical fields and the construction of physical states in the presence of an adiabatically switched off interaction.

THE UNIVERSAL EQUATIONS OF MOTION FOR NONLINEAR FIELDS IN DIFFERENT BASES DESCRIBING STRONGLY INTERACTING MANY-BODY SYSTEMS WITH TWO-BODY INTERACTIONS

1995 ◽  
Vol 09 (13n14) ◽  
pp. 1611-1637 ◽  
Author(s):  
J.M. DIXON ◽  
J.A. TUSZYŃSKI
Keyword(s):  
Plane Wave ◽  
Coherent Structures ◽  
Equations Of Motion ◽  
Quantum Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Highly Nonlinear ◽  
Many Body Systems ◽  
Definition Of

A brief account of the Method of Coherent Structures (MCS) is presented using a plane-wave basis to define a quantum field. It is also demonstrated that the form of the quantum field equations, obtained by MCS, although highly nonlinear for many-body systems with two-body interactions, is independent of the basis of states used for the definition of the field.

scholarly journals Sine-Gordon breather form factors and quantum field equations

2002 ◽  
Vol 35 (43) ◽  
pp. 9081-9104 ◽  
Author(s):  
H Babujian ◽  
M Karowski
Keyword(s):  
Form Factors ◽  
Quantum Field ◽  
Field Equations

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.

On a semi-group approach to quantum field equations

1971 ◽  
Vol 2 (1) ◽  
pp. 122-138 ◽  
Author(s):  
E. Salusti ◽  
A. Tesei
Keyword(s):  
Quantum Field ◽  
Semi Group ◽  
Field Equations ◽  
Group Approach

A priori quantum field equations

1989 ◽  
Vol 192 (1) ◽  
pp. 2-20 ◽  
Author(s):  
Arthur Jaffe ◽  
Andrzej Lesniewski ◽  
Christian Wieczerkowski
Keyword(s):  
A Priori ◽  
Quantum Field ◽  
Field Equations

scholarly journals Relation between Einstein and quantum field equations

1998 ◽  
Vol 57 (12) ◽  
pp. 7327-7339 ◽  
Author(s):  
Leonard Parker ◽  
Alpan Raval
Keyword(s):  
Quantum Field ◽  
Field Equations

Quantum gravity and renormalization

2015 ◽  
Vol 30 (03n04) ◽  
pp. 1540004 ◽  
Author(s):  
Damiano Anselmi
Keyword(s):  
Quantum Gravity ◽  
Point Of View ◽  
Quantum Field ◽  
Conformally Flat ◽  
Field Equations ◽  
Classical Action ◽  
Locally Conformally Flat ◽  
Arbitrary Dimensions ◽  
Conformally Flat Metrics ◽  
Physical Quantities

The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of non-renormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which also can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions d>3. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

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.

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