Schwinger

If we know the Green function of the non-perturbed problem, we can found a solution by using the Lippman-Schwinger integral equation ... 

Kouri D J, Huang Y, Zhu W and Hoffman D K 1994 Variational principles for the time-independent wave-packet-Schrddinger and wave-packet-Lippmann-Schwinger equations J. Chem. Phys. 100... 

The Schwinger filter, shown in Fig. XI1,2, 17, finds application when dealing with very small quantities of crystals. The solid collects as a pellet above the small filter paper disc at the throat of the filter after dismantling, the pellet may be expelled by a snugly fitting glass rod. 

J. Ogorka, G. Schwinger, G. Bmat and V. Seidel, On-line coupled reversed-phase high-performance liquid cliromatography-gas chromatography-mass specti ometi y , A powerful tool for the identification of unknown impurities in pharmaceutical products , J. Chromatogr. 626 87-96 (1992). 

R Wessels, J. Ogorka, G. Schwinger and M. Ulmer, Elucidation of the structure of drug degradation products by on-line coupled reversed phase HPEC-GC-MS and on-line deiivatization , J. High Resolut. Chromatogr. 16 708-712 (1993). 

The basic equations to be used are the Lippmann-Schwinger equations for the alloy wave function... 

Schwinger, J., Selected papers on Quantum Electrodynamics, Dover Publications, New York, 1958 (see particularly Schwinger s preface). 

This result was first obtained by Schwinger.18 The a3 contribution to F2(0) has been calculated by Sommerfield18 and by Petermann, and the result is that... 

Eq. (2.16) is not an entirely new result. After this work had been concluded and we were looking around in search of bibliographical material, we came upon a paper by Englert and Schwinger [24] dealing with the introduction of quantum corrections to the Thomas-Fermi statistical atom. These authors attain the same result expressed by eq. (2.16) (for... 

Lippmann BA, Schwinger J (1950) Variation principle for scattering processes I. Phys Rev... 

Since the non-tilde operators describe physical variables, G(k (3)11 is the physical propagator to be used to treat the properties of the thermal bosonic system. It is interesting to observe that, except for the non-diagonal elements, this TFD-propagator is equal to the one introduced in the Schwinger-Keldysh approach, which is claimed to be (in this equivalence with TFD) a thermal theory describing linear-response processes only (H. Chu et.al., 1994). 

Such equation is termed the KMS (Kubo, Martin and Schwinger) relation and describes the conditions of periodicity to be obeyed by a correlation, in particular the Green functions. 

To describe nonequilibrium phase transitions, there have been developed many methods such as the closed-time path integral by Schwinger and Keldysh (J. Schwinger et.al., 1961), the Hartree-Fock or mean field method (A. Ringwald, 1987), and the l/lV-expansion method (F. Cooper et.al., 1997 2000). In this talk, we shall employ the so-called Liouville-von Neumann (LvN) method to describe nonequilibrium phase transitions (S.P. Kim et.al., 2000 2002 2001 S.P. Kim et.al., 2003). The LvN method is a canonical method that first finds invariant operators for the quantum LvN equation and then solves exactly the... 

General Time-to-Energy Transform of Wavepackets. Time-Independent Wavepacket-Schroedinger and Wavepacket-Lippmann-Schwinger Equations. 

Energy-Separable Polynomial Representation of the Time-Independent Full Green Operator with Application to Time-Independent Wavepacket Forms of Schrodinger and Lippmann-Schwinger Equations. 

Variational Principles for the Time-Independent Wave-Packet-Schrodinger and Wave-Packet-Lippmann-Schwinger Equations. 

However, it can be argued that appropriate approximate solutions of the Schwinger-Dyson equations can yield reasonable approximations for Q, or the pressure, see the schematic Figure 1. 

Similar values for the maximal mass and radius were found in a perturbative approach with a physically motivated choice of the renormalization scale [17]. In a Schwinger-Dyson approach [18], M rb 0.7Msun and R 9 km were obtained. 

The effect of thermal pion fluctuations on the specific heat and the neutrino emissivity of neutron stars was discussed in [27, 28] together with other in-medium effects, see also reviews [29, 30], Neutron pair breaking and formation (PBF) neutrino process on the neutral current was studied in [31, 32] for the hadron matter. Also ref. [32] added the proton PBF process in the hadron matter and correlation processes, and ref. [33] included quark PBF processes in quark matter. PBF processes were studied by two different methods with the help of Bogolubov transformation for the fermion wave function [31, 33] and within Schwinger-Kadanoff-Baym-Keldysh formalism for nonequilibrium normal and anomalous fermion Green functions [32, 28, 29],... 

However, the domain of the QCD phase diagram where neutron star conditions are met is not yet accessible to Lattice QCD studies and theoretical approaches have to rely on nonperturbative QCD modeling. The class of models closest to QCD are Dyson-Schwinger equation (DSE) approaches which have been extended recently to finite temperatures and densities [11-13], Within simple, infrared-dominant DSE models early studies of quark stars [14] and diquark condensation [15] have been performed. 

To provide a realization for the algebra U(2) we take two boson creation and annihilation operators, which we denote by ot, Tr and 0,x. The algebra U(2) has four operators which can be realized as (Schwinger, 1965),... 

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