Schwinger model Green functions with topological effects

Radożycki, Tomasz

doi:10.1103/physrevd.60.105027

Cited by 13 publications

(46 citation statements)

References 26 publications

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“…That this information is contained follows directly from the fact that the exact correlation functions are sufficient to reconstruct the complete generating functional using the equality (17) [2], and in turn the correlation functions are fully described by the functional equations by virtue of the relation (12) [34]. In particular cases, this has even been demonstrated explicitly for solvable models [13,343].…”

Section: Relations To Topological Structuresmentioning

confidence: 98%

Gauge bosons at zero and finite temperature

2013

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Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

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Section: Relations To Topological Structuresmentioning

confidence: 98%

Gauge bosons at zero and finite temperature

2013

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“…However, knowing the full four-point function is usually as unlikely as solving exactly the Bethe-Salpeter equation itself. One should then all the more appreciate the SM, for which the exact form of the Green's function in question, was found [2,8]. This is the main reason, why we decided to look for the bound state singularity in this model, to analyze the nature of this singularity, and to derive the formula for the Bethe-Salpeter function.…”

Section: Introductionmentioning

confidence: 99%

“…To that category belong the products of fermion fields and, consequently, we may expect the appearance of certain new terms in the Green's functions involving quarks. The explicit calculations for the two-and fourpoint functions has been done in [16], where these supplementary terms were explicitly given. Now the question arises if, and how, these contributions modify the behaviour of the two-fermion Green's function close to the bound state singularity.…”

Section: Introductionmentioning

confidence: 99%

Instanton modifications of the bound state singularity in the Schwinger model

Radożycki

2007

Phys. Rev. D

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We consider the quark-antiquark Green's function in the Schwinger Model with instanton contributions taken into account. Thanks to the fact that this function may analytically be found, we draw out singular terms, which arise due to the formation of the bound state in the theorythe massive Schwinger boson. The principal term has a pole character. The residue in this pole contains contributions from various instanton sectors: 0, ±1, ±2. It is shown, that the nonzero ones change the factorizability property. The formula for the residue is compared to the Bethe-Salpeter wave function found as a field amplitude. Next, it is demonstrated, that apart from polar part, there appears in the Green's function also the weak branch point singularity of the logarithmic and dilogarithmic nature. These results are not in variance with the universally adopted S-matrix factorization.

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“…Massless fermions, dealt with in the present paper, suppress tunneling, but the θ -vacuum (5) still retain their importance, because topological vacua, contrary to |θ , do not exhibit the cluster decomposition property [30][31][32]34,36,38,39]. However, due to the lack of tunneling, while calculating the vacuum expectation values θ |Ô|θ , only operatorsÔ which change N (or chirality, which is equivalent [36,37]) gain off-diagonal, i.e.…”

Section: Simple Description Of the Modelmentioning

confidence: 99%

Lorentz contraction of the equal-time Bethe–Salpeter amplitude in two-dimensional massless quantum electrodynamics

Radożycki

2015

Eur. Phys. J. C

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The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in the twodimensional massless quantum electrodynamics (the socalled Schwinger model) are considered. It is shown that while boosting a bound state (a 'meson') this amplitude is subject to approximate Lorentz contraction. The effect is exact for large separations of constituent particles ('quarks'), while for small distances the deviation is more significant. For this phenomenon to appear, the full function, i.e. with the inclusion of all instanton contributions, has to be considered. The amplitude in each separate topological sector does not exhibit such properties.

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Schwinger model Green functions with topological effects

Cited by 13 publications

References 26 publications

Gauge bosons at zero and finite temperature

Gauge bosons at zero and finite temperature

Instanton modifications of the bound state singularity in the Schwinger model

Lorentz contraction of the equal-time Bethe–Salpeter amplitude in two-dimensional massless quantum electrodynamics

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