Gauge Invariant Chromoelectromagnetic Field and Hot Gluon Plasma Oscillations

Catani, Stefano; d’Emilio, Emilio

doi:10.1002/prop.19930410307

Cited by 7 publications

(9 citation statements)

References 72 publications

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“…For example, in the case of the fermion propagator S(x, y) = 0|ψ(x)ψ(y)|0 the corresponding gauge-invariant propagator S P O reads ("PO" stands for "path-ordered") S P O (x, y) = 0|ψ(x)P exp i Is this gauge-invariant propagator related in any way to the PT fermion propagator, constructed in Section 2? Of course, completely related to this question is the construction presented in [255]; in fact, the distinction made there between the Wightman and the causal two-point function might be worth pursuing from the PT point of view. Anyone remotely familiar with the PT gets the tantalizing feeling that, in addition to the BRST symmetry, some other powerful (yet undiscovered) mechanism must be at work, enforcing the PT properties.…”

Section: Discussionmentioning

confidence: 99%

Pinch technique: Theory and applications

2009

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We review the theoretical foundations and the most important physical applications of the Pinch Technique (PT). This general method allows the construction of off-shell Green's functions in non-Abelian gauge theories that are independent of the gauge-fixing parameter and satisfy ghost-free Ward identities. We first present the diagrammatic formulation of the technique in QCD, deriving at one loop the gauge independent gluon self-energy, quark-gluon vertex, and three-gluon vertex, together with their Abelian Ward identities. The generalization of the PT to theories with spontaneous symmetry breaking is carried out in detail, and the profound connection with the optical theorem and the dispersion relations are explained within the electroweak sector of the Standard Model. The equivalence between the PT and the Feynman gauge of the Background Field Method (BFM) is elaborated, and the crucial differences between the two methods are critically scrutinized. A variety of field theoretic techniques needed for the generalization of the PT to all orders are introduced, with particular emphasis on the Batalin-Vilkovisky quantization method and the general formalism of algebraic renormalization. The main conceptual and technical issues related to the extension of the technique beyond one loop are described, using the twoloop construction as a concrete example. Then the all-order generalization is thoroughly examined, making extensive use of the field theoretic machinery previously introduced; of central importance in this analysis is the demonstration that the PT-BFM correspondence persists to all orders in perturbation theory. The extension of the PT to the non-perturbative domain of the QCD Schwinger-Dyson equations is presented systematically, and the main advantages of the resulting self-consistent truncation scheme are discussed. A plethora of physical applications relying on the PT are finally reviewed, with special emphasis on the definition of gauge-independent off-shell form-factors, the construction of non-Abelian effective charges, the gauge-invariant treatment of resonant transition amplitudes and unstable particles, and finally the dynamical generation of an effective gluon mass.

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Section: Discussionmentioning

confidence: 99%

Pinch technique: Theory and applications

2009

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“…In particular one could study the precise cancellation mechanism of the infrared divergences using a proper infrared regularization scheme, and explicit expressions for the two-and three-gluon phase-space, which we have not needed here. In addition, it would be interesting to attempt a similar two-loop derivation using the formalism developed in [59], and study possible connections.…”

Section: Discussionmentioning

confidence: 99%

Pinch technique at two loops: The case of massless Yang-Mills theories

Papavassiliou

2000

Phys. Rev. D

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The generalization of the pinch technique beyond one loop is presented. It is shown that the crucial physical principles of gauge-invariance, unitarity, and gauge-fixing-parameter independence are instrumental for accomplishing this task, and is explained how the aforementioned requirements single out at two loops exactly the same algorithm which has been used to define the pinch technique at one loop, without any additional assumptions. The two-loop construction of the pinch technique gluon self-energy, and quark-gluon vertex are carried out in detail for the case of mass-less YangMills theories, such as perturbative QCD. We present two different but complementary derivations. First we carry out the construction by directly rearranging two-loop diagrams. The analysis reveals that, quite interestingly, the well-known one-loop correspondence between the pinch technique and the background field method in the Feynman gauge persists also at two-loops. Since we use dimensional regularization the entire construction does not depend on the value of the space-time dimension d. The renormalization (when d = 4) is discussed in detail, and is shown to respect the aforementioned correspondence. Second, we present an absorptive derivation, exploiting the unitarity of the S-matrix and the underlying BRS symmetry; at this stage we deal only with tree-level and one-loop physical amplitudes. The gauge-invariant sub-amplitudes defined by means of this absorptive construction correspond precisely to the imaginary parts of the n-point functions defined in the full two-loop derivation, thus furnishing a highly nontrivial self-consistency check for the entire method. Various future applications are briefly discussed.

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“…Furthermore, at the conceptual level it is unknown whether a formal definition of the PT Green's functions in terms of fundamental fields, encoding "ab initio" their special properties, is possible. Finally, it would be interesting to explore possible connections with various related formalisms [55,56,57,58,59].…”

Section: Discussionmentioning

confidence: 99%

Pinch technique self-energies and vertices to all orders in perturbation theory

Binosi

Papavassiliou

2004

J. Phys. G: Nucl. Part. Phys.

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The all-order construction of the pinch technique gluon self-energy and quark-gluon vertex is presented in detail within the class of linear covariant gauges. The main ingredients in our analysis are the identification of a special Green's function, which serves as a common kernel to all self-energy and vertex diagrams, and the judicious use of the Slavnov-Taylor identity it satisfies. In particular, it is shown that the ghost-Green's functions appearing in this identity capture precisely the result of the pinching action at arbitrary order. By virtue of this observation the construction of the quarkgluon vertex becomes particularly compact. It turns out that the aforementioned ghost-Green's functions play a crucial role, their net effect being the non-trivial modification of the ghost diagrams of the quark-gluon vertex in such a way as to reproduce dynamically the characteristic ghost sector of the background field method. The gluon self-energy is also constructed following two different procedures. First, an indirect derivation is given, by resorting to the strong induction method and the assumption of the uniqueness of the S-matrix. Second, an explicit construction based on the intrinsic pinch technique is provided, using the Slavnov-Taylor identity satisfied by the all-order three-gluon vertex nested inside the self-energy diagrams. The process-independence of the gluon self-energy is also demonstrated, by using gluons instead of quark as external test particles, and identifying the corresponding kernel function, together with its Slavnov-Taylor identity. Finally, the general methodology for carrying out the renormalization of the resulting Green's functions is outlined, and various open questions are briefly discussed.

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Gauge Invariant Chromoelectromagnetic Field and Hot Gluon Plasma Oscillations

Cited by 7 publications

References 72 publications

Pinch technique: Theory and applications

Pinch technique: Theory and applications

Pinch technique at two loops: The case of massless Yang-Mills theories

Pinch technique self-energies and vertices to all orders in perturbation theory

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