Functional integrals and inequivalent representations in Quantum Field Theory

2017 ◽  
Vol 383 ◽  
pp. 207-238 ◽  
Author(s):  
M. Blasone ◽  
P. Jizba ◽  
L. Smaldone
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Functional Integrals ◽  
Inequivalent Representations

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.

scholarly journals The Philosophy of Quantum Field Theory

2016 ◽  
Author(s):  
David John Baker
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
State Space ◽  
Traditional View ◽  
Quantum Field ◽  
Inequivalent Representations ◽  
Cpt Theorem ◽  
Particle Interpretation

This is an opinionated survey of some interpretive puzzles in quantum field theory. The problem of inequivalent representations is sketched, including its connections with competing accounts of physical equivalence. The controversy between variant formulations of the theory, algebraic versus Lagrangian, is given a conciliatory resolution. Arguments against particles are addressed, demarcating clearly between different forms of particle interpretation. Field interpretations are then considered, including wavefunctional, spacetime state realist and Heisenberg operator realist interpretations. Ruetsche’s coalesced structure interpretation is presented and juxtaposed with an alternative, more traditional view of the theory’s laws and state space. Finally, the CPT theorem is discussed, together with its implications about the nature of spacetime.

On functional integrals in quantum field theory

1991 ◽  
Vol 29 (1) ◽  
pp. 101-108 ◽  
Author(s):  
G. Sardanashvily ◽  
O. Zakharov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Functional Integrals

Functional integrals

2021 ◽  
pp. 117-146
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Functional Integral ◽  
Quantum Field ◽  
Functional Integrals ◽  
Generating Functional ◽  
Curved Space ◽  
Functional Representation ◽  
Alternative Approach ◽  
The Subject

This chapter presents an alternative approach to the quantization of fields, an approach that will be critically important for the development of quantum field theory in curved space, which is the subject of the second part of the book. It starts by providing a description of a functional integral in quantum mechanics, concentrating on the representation of an evolution operator. It then considers the functional representation of the Green functions and the generating functional in quantum field theory, including for fermionic theories. After that, perturbative calculations of the generating functionals and their general properties are formulated. The chapter ends with a brief description of ζ‎-regularization as a technique for defining functional determinants.

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