共查询到20条相似文献,搜索用时 31 毫秒
1.
T. S. Evans 《Zeitschrift fur Physik C Particles and Fields》1988,41(2):333-339
Using path integral techniques, it is shown that the real time formalism for finite temperature field theory requires an extra Feynman rule for Feynman diagrams carrying zero-external energies. This is related to a general principle governing the use of equilibrium finite temperature field theory. It is shown that only with this extra Feynman rule does the real time formalism become consistent for zero energy calculations. It is also used to understand the problem of the lack of analyticity at zero external four-momenta encountered in finite temperature field theory diagrams. 相似文献
2.
The consistency of loop regularization (LORE) method is explored in multiloop calculations. A key concept of the LORE method is the introduction of irreducible loop integrals (ILIs) which are evaluated from the Feynman diagrams by adopting the Feynman parametrization and ultraviolet-divergence-preserving (UVDP) parametrization. It is then inevitable for the ILIs to encounter the divergences in the UVDP parameter space due to the generic overlapping divergences in the four-dimensional momentum space. By computing the so-called αβγ integrals arising from two-loop Feynman diagrams, we show how to deal with the divergences in the parameter space with the LORE method. By identifying the divergences in the UVDP parameter space to those in the subdiagrams, we arrive at the Bjorken–Drell analogy between Feynman diagrams and electrical circuits. The UVDP parameters are shown to correspond to the conductance or resistance in the electrical circuits, and the divergence in Feynman diagrams is ascribed to the infinite conductance or zero resistance. In particular, the sets of conditions required to eliminate the overlapping momentum integrals for obtaining the ILIs are found to be associated with the conservations of electric voltages, and the momentum conservations correspond to the conservations of electrical currents, which are known as the Kirchhoff laws in the electrical circuits analogy. As a practical application, we carry out a detailed calculation for one-loop and two-loop Feynman diagrams in the massive scalar ? 4 theory, which enables us to obtain the well-known logarithmic running of the coupling constant and the consistent power-law running of the scalar mass at two-loop level. Especially, we present an explicit demonstration on the general procedure of applying the LORE method to the multiloop calculations of Feynman diagrams when merging with the advantage of Bjorken–Drell’s circuit analogy. 相似文献
3.
A. P. Isaev 《Physics of Atomic Nuclei》2008,71(5):914-924
The operator approach to analytical evaluation of multiloop Feynman diagrams is proposed. We show that the known analytical
methods of evaluation of massless Feynman integrals, such as the integration-by-parts method and the method of “uniqueness”
(which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate
the advantages of the operator method of analytical evaluation of multiloop Feynman diagrams, we calculate ladder diagrams
for the massless ϕ
3 theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator
formalism can be applied to calculation of certain massive Feynman diagrams and investigation of the Lipatov integrable chain
model.
The text was submitted by the authors in English. 相似文献
4.
在热场动力学的框架下,依据有限温度下的切割定理提出了一套直观的费曼图切割方法及其相应的费曼规则,从而给出了一条计算热格林函数应部的方便途径.作为应用的例子我们分别讨论了二点、三点和四点格林函数的虚部. 相似文献
5.
《Nuclear Physics B》2003,662(3):461-475
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts and star-triangle relation methods, can be drastically simplified by using this algebraic approach. To demonstrate the advantages of the algebraic method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless φ3 theory. Using our algebraic approach we show that the problem of evaluation of special classes of Feynman diagrams reduces to the calculation of the Green functions for specific quantum mechanical problems. In particular, the integrals for ladder massless diagrams in the φ3 scalar field theory are given by the Green function for the conformal quantum mechanics. 相似文献
6.
K. A. James 《Zeitschrift fur Physik C Particles and Fields》1991,49(1):115-121
Using the 2×2 matrix propagator previously found by the author, we calculate the interaction pressure of the gluon plasma to two loops at high temperature using the temporal axial gauge in the real time formalism. This quantity is gauge invariant and is thus a good check for the validity of the Feynman rules found for the temporal gauge at finite temperature. Our result is identical to that found by Landsman et al. and Kapusta using covariant gauges in the real and imaginary time formalisms respectively. 相似文献
7.
We formulate finite-temperature quantum field theories in Minkowski space (real time) using Feynman path integrals. We show that at non-zero temperature a new field arises which plays the role of a ghost field and is necessary for unambiguous Feynman rules. Consequently, the finite-temperature Lagrangian is different from the zero-temperature one and a new, discrete Z2 symmetry arises. We discuss the functional formalism and spontaneous symmetry breakdown at finite temperature and also the possibility of spontaneous breakdown of the (thermal) Z2 symmetry. 相似文献
8.
K. A. James 《Zeitschrift fur Physik C Particles and Fields》1990,48(1):169-182
The temporal axial gauge is discussed at zero temperature and extended to finite temperature. A set of Feynman rules is determined within the real-time formalism which allows one to do perturbation theory at finite temperature using the temporal gauge. As a demonstration of the Feynman rules derived we do a simple linear response analysis for the gluon plasma at high temperature. This analysis yields a positive damping constant to one loop order in the long-wavelength limit. The problem of the imaginary-time formalism is discussed. 相似文献
9.
We continue our discussion of the background field formalism in supersymmetric theories, deriving new covariant Feynman rules for chiral superfields. As a result, we obtain improved power-counting rules for both simple and extended supersymmetry which can be used to make the following statements: If the corresponding extended superfield formalism exist, (a) N=2 supersymmetric Yang-Mills theory is finite beyond one loop, (b) N=4 Yang-Mills is finite at all loops, and (c) N=8 supergravity is finite through six loops. We also find that in simple super-Yang-Mills the radiative corrections to the Fayet-Iliopoulos (“D”) term, which are known to vanish for higher loops, also vanish automatically at one loop for arbitrary couplings. 相似文献
10.
J. Fleischer V. A. Smirnov O. V. Tarasov 《Zeitschrift fur Physik C Particles and Fields》1997,74(2):379-386
A method of calculating Feynman diagrams from their small momentum expansion [1] is extended to diagrams with zero mass thresholds. We start from the asymptotic expansion in large masses [2] (applied to the case when all $M_i^2$ are large compared to all momenta squared). Using dimensional regularization, a finite result is obtained in terms of powers of logarithms (describing the zero-threshold singularity) times power series in the momentum squared. Surprisingly, these latter ones represent functions, which not only have the expected physical “second threshold” but have a branchcut singularity as well below threshold at a mirror position. These can be understood as pseudothresholds corresponding to solutions of the Landau equations. In the spacelike region the imaginary parts from the various contributions cancel. For the two-loop examples with one mass M, in the timelike region for q2 ≈ M2 we obtain approximations of high precision. This will be of relevance in particular for the calculation of the decay Z → bb?in the m b = 0 approximation. 相似文献
11.
12.
Using the Feynman parameter method, we have calculated in an elegant manner a set of one-loop box scalar integrals with massless
internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and collinear), the
dimensional regularization method has been employed. The results for these integrals, which appear in the process of evaluating
one-loop -point integrals and in subdiagrams in QCD loop calculations, have been obtained for arbitrary values of the relevant kinematic
variables and are presented in a simple and compact form.
Received: 8 March 2001 / Published online: 18 May 2001 相似文献
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15.
The one-loop expression for the absorptive correction to the πd scattering length is discussed. Relevant Feynman diagrams are calculated both in the relativistic and in the nonrelativistic formalism. A simple expression is obtained for the one-loop correction that arises in the πd scattering length owing to the Fermi motion of the nucleons in the deuteron. This correction includes absorption effects. Fulfillment of the unitarity relation is verified explicitly. 相似文献
16.
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases in their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their numerical evaluation in the general case of D-dimensional space-time as well as in integer dimensions D = D0 for different values of dimensions including the most important practical cases D0 = 2, 3, 4. Substantial simplifications occur for odd integer space-time dimensions where the final results can be expressed in closed form through elementary functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology where an irreducible loop is added. 相似文献
17.
《Physics Reports》1988,170(3):167-212
18.
Predrag Cvitanović C. P. Dettmann Ronnie Mainieri Gábor Vattay 《Journal of statistical physics》1998,93(3-4):981-999
Periodic orbit theory is all effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory is cast in the standard field-theoretic formalism and weak noise perturbation theory written in terms of Feynman diagrams. The result is a stochastic analog of the next-to-leading ? corrections to the Gutzwiller trace formula, with long-time averages calculated from periodic orbits of the deterministic system. The perturbative corrections are computed analytically and tested numerically on a simple 1-dimensional system. 相似文献
19.
We examine in detail the techniques of supersymmetric dimensional regularization. A peculiar complementarity is found to be inherent in the regularization: its manifestly supersymmetric version is contradictory, while the removal of inconsistencies costs a lossof supersymmetry in higher orders. We analyse this phenomenon at the level of Feynman diagrams and discover an explicit example of supersymmetry breakdown in the three-loop approximation. In the light of this result, we reconsider the status of dimensional regularization in globally supersymmetric gauge theories. 相似文献
20.
P.G. Ratcliffe 《The European Physical Journal C - Particles and Fields》1999,8(3):403-408
We analyse the twist-three amplitudes that can give rise to single-spin asymmetries in hadron-hadron scattering; in so doing
we bring to light a novel factorisation property. As already known, the requirement of an imaginary part leads to consideration
of twist-three contributions that are also related to transverse spin in deep-inelastic scattering. In particular, when an
external line becomes soft in contributions arising from three-parton correlators, the imaginary part of an internal propagator
may be exposed. As shown here, it is precisely this kinematical configuration that permits the factorisation. An important
feature is the resulting simplification: the calculation of tens of Feynman diagrams normally contributing to such processes
is reduced to the evaluation of products of the simple factors derived here and known two-body helicity amplitudes. We thus
find clarifying relations between the spin-dependent and spin-averaged cross-sections and formulate a series of selection
rules. In addition, the kinematical dependence of such asymmetries, is rendered more transparent.
Received: 31 July 1998 / Revised version: 12 November 1998 / Published online: 11 March 1999 相似文献