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Lagrangian relativistic

A covariant Lagrangian density (i.e. an equation that looks the same in all Lorentz frames) will be obtained if the Lagrangian density is defined in terms of a relativistic scalar density, as in... [Pg.156]

A description of nuclear matter as an ideal mixture of protons and neutrons, possibly in (5 equilibrium with electrons and neutrinos, is not sufficient to give a realistic description of dense matter. The account of the interaction between the nucleons can be performed in different ways. For instance we have effective nucleon-nucleon interactions, which reproduce empirical two-nucleon data, e.g. the PARIS and the BONN potential. On the other hand we have effective interactions like the Skyrme interaction, which are able to reproduce nuclear data within the mean-field approximation. The most advanced description is given by the Walecka model, which is based on a relativistic Lagrangian and models the nucleon-nucleon interactions by coupling to effective meson fields. Within the relativistic mean-field approximation, quasi-particles are introduced, which can be parameterized by a self-energy shift and an effective mass. [Pg.80]

FM at some density 1. One of the essential points we learned here is that we need no spin-dependent interaction at the original Lagrangian to see SSP. We can see a similar phenomenon in dealing with nuclear matter within the relativistic mean-field theory, where the Fock interaction can be extracted by way of the Fierz transformation from the original Lagrangian [11],... [Pg.244]

To calculate the nucleation rate of quark matter in the hadronic medium we use the Lifshitz-Kagan quantum nucleation theory (Lifshitz Kagan 1972) in the relativistic form given by Iida Sato (1997). The QM droplet is supposed to be a sphere of radius 72 and its quantum fluctuations are described by the Lagrangian... [Pg.359]

All solutions of this Hamiltonian are thereby electronic, whether they are of positive or negative energy and contrary to what is often stated in the literature. Positronic solutions are obtained by charge conjugation. From the expectation value of the Dirac Hamiltonian (23) and from consideration of the interaction Lagrangian (16) relativistic charge and current density are readily identified as... [Pg.390]

Nonrelativistic quantum electrodynamics (NRQED) [11] is an attempt to combine the simplicity of the quantum mechanical description with the power and rigor of field theory. The idea is to write ordinary relativistic quantum electrodynamics in the form of a nonrelativistic expansion with a Lagrangian containing vertices with arbitrary powers of fields. This is useful if we want to consider essentially nonrelativistic processes, like nonrelativistic bound states and threshold phenomena. In such a physical situation the dominant dynamics is nonrelativistic, and the calculations could be in principle simplified if... [Pg.10]

In formulating QED a least-action principle involving a Lagrangian is often used [9,18,20]. This involves the potentials in various forms. Not only is relativistic invariance (Lorenz potentials) desired, but also gauge invariance. At least in the current state of QED, gauge invariance is included as a fundamental part [21,22]. [Pg.618]

J. P. Vigier, F. Halbwachs, and P. Hillion, Quadratic Lagrangians in relativistic hydrodynamics, Nuovo Cimento 11, 882 (1959). [Pg.195]

This section will be broken into a number of discussions. The first will be on a naive 5(7(2) x 5(7(2) extended standard model, followed by a more general chiral theory and a discussion on the lack of Lagrangian dynamics associated with the B3 field. This will be followed by an examination of non-Abelian QED at nonrelativistic energies and then at relativistic energies. It will conclude with a discussion of a putative 5(9(10) gauge unification that includes the strong interactions. [Pg.406]

This paper presents an account of the dynamics of electric charges coupled to electromagnetic fields. The main approximation is to use non-relativistic forms for the charge and current density. A quantum theory requires either a Lagrangian or a Hamiltonian formulation of the dynamics in atomic and molecular physics the latter is almost universal so the main thrust of the paper is the development of a general Hamiltonian. It is this Hamiltonian that provides the basis for a recent demonstration that the S-matrix on the energy shell is gauge-invariant to all orders of perturbation theory. [Pg.4]

The variational formalism makes it possible to postulate a relativistic Lagrangian that is Lorentz invariant and reduces to Newtonian mechanics in the classical limit. Introducing a parameter m, the proper mass of a particle, or mass as measured in its own instantaneous rest frame, the Lagrangian for a free particle can be postulated to have the invariant form A = mulxiilx = — mc2. The canonical momentum is pf, = iiiuj, and the Lagrangian equation of motion is... [Pg.21]

Given the electromagnetic 4-vector field A/( = (A, i(p) and the 4-velocity m/( = (yv, iyc), W is the classical limit of a relativistic invariant y W = A u. This term augments the tree-particle relativistic Lagrangian to give... [Pg.23]

Noether s theorem will be proved here for a classical relativistic theory defined by a generic field , which may have spinor or tensor indices. The Lagrangian density (, 9/x) is assumed to be Lorentz invariant and to depend only on scalar forms defined by spinor or tensor fields. It is assumed that coordinate displacements are described by Jacobi s theorem S(d4x) = d4x 9/xgeneral variation of the action integral, evaluated over a closed space-time region 2, is... [Pg.186]

Relativistic Lagrangian theories 10.3.3 Nonabelian gauge symmetries... [Pg.192]

Relativistic Lagrangian theories implying the gauge field equations... [Pg.196]

In non-relativistic classical mechanics a mechanical system can be characterised by a function called the Lagrangian, S(q, q) where q denotes the coordinates, and the motion of the system is such that the action S, defined by... [Pg.68]

An electromagnetic field is described in relativistic theory by a four-vector A, where the three space components Aij2,3 = Aare called the vector potential A and the fourth (time) component A4 is equal to i where

scalar potential. The Lagrangian for a particle in an electromagnetic field is now given by... [Pg.69]

It was pointed out in chapter 1 that there exist alternative mean-field theories to the Hartree-Fock method. In particular, one of these, the <7-Hartree method, is a fully relativistic theory which determines the optimum mean field in such a way as to make the Lagrangian of quantum field theory stationary. This is a fundamental choice, but turns out [230] to be satisfied by a whole family of SCF potentials of the general form... [Pg.170]


See other pages where Lagrangian relativistic is mentioned: [Pg.318]    [Pg.359]    [Pg.384]    [Pg.389]    [Pg.152]    [Pg.1395]    [Pg.22]    [Pg.315]    [Pg.20]    [Pg.179]    [Pg.181]    [Pg.181]    [Pg.182]    [Pg.184]    [Pg.186]    [Pg.188]    [Pg.190]    [Pg.194]    [Pg.198]    [Pg.200]    [Pg.202]    [Pg.245]    [Pg.74]    [Pg.5]    [Pg.200]    [Pg.125]   
See also in sourсe #XX -- [ Pg.21 ]

See also in sourсe #XX -- [ Pg.363 ]




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