Functional integral formulation of field theory

2014 ◽  
pp. 35-40
Keyword(s):  
Field Theory ◽  
Functional Integral ◽  
Integral Formulation

scholarly journals Some comments on infinities on quantum field theory: A functional integral approach

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Luiz C. L. Botelho
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Function Space ◽  
Functional Integral ◽  
Field Theories ◽  
Integral Approach ◽  
Quantum Field ◽  
Functional Integrals ◽  
Euclidean Field ◽  
The Subject

AbstractWe analyze on the formalism of probabilities measures-functional integrals on function space the problem of infinities on Euclidean field theories. We also clarify and generalize our previous published studies on the subject.

CORRELATION FUNCTIONS OF σ FIELDS WITH VALUES IN A HYPERBOLIC SPACE

1989 ◽  
Vol 04 (01) ◽  
pp. 267-286 ◽  
Author(s):  
Z. HABA
Keyword(s):  
Field Theory ◽  
Hyperbolic Space ◽  
Half Plane ◽  
Correlation Functions ◽  
Functional Integral ◽  
Two Dimensions ◽  
Hyperbolic Spaces ◽  
Conformal Invariant ◽  
Upper Half Plane

It is shown that the functional integral for a σ field with values in the Poincare upper half-plane (and some other hyperbolic spaces) can be performed explicitly resulting in a conformal invariant noncanonical field theory in two dimensions.

CONFORMALLY INVARIANT FIELD THEORY IN TWO DIMENSIONS AND STRINGS IN CURVED SPACETIME

1988 ◽  
Vol 03 (08) ◽  
pp. 1759-1846 ◽  
Author(s):  
SANJAY JAIN
Keyword(s):  
Field Theory ◽  
Equations Of Motion ◽  
Virasoro Algebra ◽  
Functional Integral ◽  
Two Dimensions ◽  
Intrinsic Metric ◽  
Existence Of A Solution ◽  
Conformally Invariant ◽  
Brst Charge ◽  
Spacetime Metric

The formalism of conformally invariant field theory on a 2-dimensional real manifold with an intrinsic metric is developed in the functional integral framework. This formalism is used to study the relationships between reparametrization, Weyl, conformal and BRST invariances for strings in generic backgrounds. Conformal invariance of string amplitudes in the presence of backgrounds is formulated in terms of the Virasoro conditions, i.e., that physical vertex operators generate (1,1) representations of the Virasoro algebra, or, equivalently, the condition Q|Ψ〉=0 on physical states |Ψ〉, where Q is the BRST charge. The consequences of these conditions are investigated in the case of specific backgrounds. Strings in group manifolds are discussed exactly. For a generic slowly varying spacetime metric and dilaton field, a perturbatively renormalized vertex operator solution to the Virasoro conditions is constructed. It is shown that the existence of a solution to the Virasoro conditions or the equation Q|Ψ〉=0 requires the spacetime metric to satisfy Einstein’s equations. These conditions therefore constitute equations of motion for both the spectrum and backgrounds of string theory.

From Classical to Quantum Fields

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Laws Of Nature ◽  
Classical Field Theory ◽  
Functional Integral ◽  
Theoretical Physics ◽  
Standard Theory ◽  
Quantum Field ◽  
Detailed Model ◽  
Universal Language

Quantum field theory has become the universal language of most modern theoretical physics. This book is meant to provide an introduction to this subject with particular emphasis on the physics of the fundamental interactions and elementary particles. It is addressed to advanced undergraduate, or beginning graduate, students, who have majored in physics or mathematics. The ambition is to show how these two disciplines, through their mutual interactions over the past hundred years, have enriched themselves and have both shaped our understanding of the fundamental laws of nature. The subject of this book, the transition from a classical field theory to the corresponding Quantum Field Theory through the use of Feynman’s functional integral, perfectly exemplifies this connection. It is shown how some fundamental physical principles, such as relativistic invariance, locality of the interactions, causality and positivity of the energy, form the basic elements of a modern physical theory. The standard theory of the fundamental forces is a perfect example of this connection. Based on some abstract concepts, such as group theory, gauge symmetries, and differential geometry, it provides for a detailed model whose agreement with experiment has been spectacular. The book starts with a brief description of the field theory axioms and explains the principles of gauge invariance and spontaneous symmetry breaking. It develops the techniques of perturbation theory and renormalisation with some specific examples. The last Chapters contain a presentation of the standard model and its experimental successes, as well as the attempts to go beyond with a discussion of grand unified theories and supersymmetry.

scholarly journals THE SPACE OF STRING CONFIGURATIONS IN STRING FIELD THEORY

1990 ◽  
Vol 05 (10) ◽  
pp. 1911-1918 ◽  
Author(s):  
JOSÈ BORDES ◽  
FEDELE LIZZI
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Sobolev Spaces ◽  
Functional Integral ◽  
Dual Model ◽  
Integrable Functions ◽  
Square Integrable Functions

In this paper we consider the set of maps from the interval [0, π] which constitute the argument of the functionals of a String Field Theory. We show that in order to correctly reproduce results of the dual model one has to include all square integrable functions in the functional integral, or Ω0 in terms of Sobolev spaces.

scholarly journals Functional integral method in quantum field theory of Dirac fermions in graphene

2017 ◽  
Vol 8 (3) ◽  
pp. 035018
Author(s):  
Nguyen Duc Duoc Phan ◽  
Nhu Dat Nguyen ◽  
Van Hau Tran ◽  
Toan Thang Nguyen ◽  
Van Hieu Nguyen
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Integral Method ◽  
Functional Integral ◽  
Dirac Fermions ◽  
Quantum Field ◽  
Functional Integral Method
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