The 0D quantum field theory: Multiple integrals via background field formalism

2016 ◽  
Author(s):  
Aleksei A. Bagaev ◽  
Yuri M. Pis'mak
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Background Field ◽  
Quantum Field ◽  
Multiple Integrals ◽  
Field Formalism

scholarly journals Scenario for the renormalization in the 4D Yang–Mills theory

2016 ◽  
Vol 31 (01) ◽  
pp. 1630001 ◽  
Author(s):  
L. D. Faddeev
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Background Field ◽  
Space Time ◽  
Quantum Field ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Field Formalism

The renormalizability of the Yang–Mills quantum field theory in four-dimensional space–time is discussed in the background field formalism.

scholarly journals Classical simulation of quantum fields I

2006 ◽  
Vol 84 (10) ◽  
pp. 861-877 ◽  
Author(s):  
T Hirayama ◽  
B Holdom
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Zero Point ◽  
Background Field ◽  
Field Configuration ◽  
Classical Electrodynamics ◽  
Quantum Field ◽  
Point Energy ◽  
Classical Simulation ◽  
Feynman Rules

We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical electrodynamics by Wheeler–Feynman and the theory of stochastic electrodynamics of Boyer. The nonperturbative effects of interactions in these theories can be very efficiently studied on the lattice. In [Formula: see text] theory in 1 + 1 dimensions, we find results, in particular, for mass renormalization and the critical coupling for symmetry breaking that are in agreement with their quantum counterparts. We then study the perturbative expansion of the n-point Green's functions and find a loop expansion very similar to that of quantum field theory. When compared to the usual Feynman rules, we find some differences associated with particular combinations of internal lines going on-shell simultaneously. PACS Nos.: 03.70.+k, 03.50.–z, 11.15.Tk

scholarly journals Acausal quantum theory for non-Archimedean scalar fields

2019 ◽  
Vol 31 (04) ◽  
pp. 1950011 ◽  
Author(s):  
M. L. Mendoza-Martínez ◽  
J. A. Vallejo ◽  
W. A. Zúñiga-Galindo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Scalar Fields ◽  
Background Field ◽  
Quantum Field ◽  
Second Quantization ◽  
Klein Gordon ◽  
Free Fields ◽  
Wightman Axioms

We construct a family of quantum scalar fields over a [Formula: see text]-adic spacetime which satisfy [Formula: see text]-adic analogues of the Gårding–Wightman axioms. Most of the axioms can be formulated in the same way for both the Archimedean and non-Archimedean frameworks; however, the axioms depending on the ordering of the background field must be reformulated, reflecting the acausality of [Formula: see text]-adic spacetime. The [Formula: see text]-adic scalar fields satisfy certain [Formula: see text]-adic Klein–Gordon pseudo-differential equations. The second quantization of the solutions of these Klein–Gordon equations corresponds exactly to the scalar fields introduced here. The main conclusion is that there seems to be no obstruction to the existence of a mathematically rigorous quantum field theory (QFT) for free fields in the [Formula: see text]-adic framework, based on an acausal spacetime.

scholarly journals Differential Dyson–Schwinger equations for quantum chromodynamics

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Marco Frasca
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Chromodynamics ◽  
Background Field ◽  
Low Energy ◽  
Quantum Field ◽  
Approximate Form ◽  
Energy Behavior ◽  
Hooft Limit ◽  
Dynamical Breaking

Abstract Using a technique devised by Bender, Milton and Savage, we derive the Dyson–Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The ’t Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.

scholarly journals Limiting fluctuations in quantum gravity to diffeomorphisms

2021 ◽  
pp. 2150197
Author(s):  
Brian Slovick
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Background Field ◽  
Quantum Corrections ◽  
Quantum Field ◽  
Classical Action ◽  
Gauge Transformations ◽  
Background Independence ◽  
Field Formalism

Within the background field formalism of quantum gravity, I show that if the quantum fluctuations are limited to diffeomorphic gauge transformations rather than the physical degrees of freedom, as in conventional quantum field theory, all the quantum corrections vanish on shell and the effective action is equivalent to the classical action. In principle, the resulting theory is finite and unitary, and requires no renormalization. I also show that this is the unique parameterization that renders the path integral independent of the on-shell condition for the background field, a form of background independence. Thus, a connection is established between background independence and renormalizability and unitarity.

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