Constructive field theory: Thirring model interaction $$(\tilde \psi \gamma \mu \tilde \psi )_2^2 $$ I. local field

We established a resummed formula for the effective potential of [Formula: see text] scalar field theory that can mimic the true effective potential not only at the critical region but also at any point in the coupling space. We first extend the effective potential from the oscillator representation method, perturbatively, up to g3 order. We supplement perturbations by the use of a resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g3 order, we found a good agreement between our resummed effective potential and the well-known features from constructive field theory. The resummed effective potential agrees well with the constructive field theory results concerning existing and order of phase transition in the absence of an external magnetic field. In the presence of the external magnetic field, as in magnetic systems, the effective potential shows nonexistence of phase transition and gives the behavior of the vacuum condensate as a monotonic increasing function of J, in complete agreement with constructive field theory methods.

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Asymptotic relations between cross sections in local field theory

Physics Letters ◽

10.1016/0031-9163(63)90446-3 ◽

1963 ◽

Vol 7 (1) ◽

pp. 69-71 ◽

Cited By ~ 48

Author(s):

A.A. Logunov ◽

Nguyen Van Hieu ◽

I.T. Todorov ◽

O.A. Khrustalev

Keyword(s):

Field Theory ◽

Cross Sections ◽

Local Field ◽

Local Field Theory

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Local Field Theory and Isospin Invariance. I. Free‐Field Theory of Spinless Bosons

Journal of Mathematical Physics ◽

10.1063/1.1664663 ◽

1968 ◽

Vol 9 (6) ◽

pp. 928-945 ◽

Cited By ~ 12

Author(s):

Peter Carruthers

Keyword(s):

Field Theory ◽

Local Field ◽

Free Field ◽

Local Field Theory

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A Yang–Mills Theory in Loop Space and Chapline–Manton Coupling

Modern Physics Letters A ◽

10.1142/s0217732397000108 ◽

1997 ◽

Vol 12 (02) ◽

pp. 111-119 ◽

Cited By ~ 2

Author(s):

Shinichi Deguchi ◽

Tadahito Nakajima

Keyword(s):

Field Theory ◽

Local Field ◽

Loop Space ◽

Tensor Field ◽

Symmetric Tensor ◽

Tensor Fields ◽

Yang Mills ◽

Local Field Theory ◽

Antisymmetric Tensor Field ◽

Chern Simons

We consider a Yang–Mills theory in loop space with the affine gauge group. From this theory, we derive a local field theory with Yang–Mills fields and Abelian antisymmetric and symmetric tensor fields of the second rank. The Chapline–Manton coupling, i.e. coupling of Yang–Mills fields and a second-rank antisymmetric tensor field via the Chern–Simons three-form is obtained systematically.

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