Field Degrees Of Freedom Research Articles

QUANTIZATION OF REDUCED CHERN–SIMONS GRAVITY WITH A SOURCE

Using the Dirac's theory of constraints, procedure of reduction of field degrees of freedom, whose number is restricted by equations of motion and topological conditions, is proposed. Such a procedure is applied in the case of space with the topology of a torus to the Chern–Simons gravity generalized by inclusion of a source. It is shown that in this system some modular transformations preserving the volume do not lead to physically equivalent states. Such a breaking of modular symmetry reduces the degeneration of quantum states with preservation of continuous spectrum of the volume operator. Probability of transition between spaces of different volumes is computed.

Computation within the auxiliary field approach

Recently, the classical auxiliary field methodology has been developed as a new simulation technique for performing calculations within the framework of classical statistical mechanics. Since the approach suffers from a sign problem, a judicious choice of the sampling algorithm, allowing a fast statistical convergence and an efficient generation of field configurations, is of fundamental importance for a successful simulation. In this paper we focus on the computational aspects of this simulation methodology. We introduce two different types of algorithms, the single-move auxiliary field Metropolis Monte Carlo algorithm and two new classes of force-based algorithms, which enable multiple-move propagation. In addition, to further optimize the sampling, we describe a preconditioning scheme, which permits to treat each field degree of freedom individually with regard to the evolution through the auxiliary field configuration space. Finally, we demonstrate the validity and assess the competitiveness of these algorithms on a representative practical example. We believe that they may also provide an interesting possibility for enhancing the computational efficiency of other auxiliary field methodologies.

ELIMINATION OF THE FIELD DEGREES OF FREEDOM IN RELATIVISTIC SYSTEM OF POINTLIKE CHARGES

The Hamiltonian formulation of relativistic system of charged particles plus electromagnetic field in the Dirac instant and front forms of dynamics is considered. The canonical realization of the Poincaré algebra in the terms of gauge-invariant variables is found. The procedure of elimination of the field degrees of freedom within the framework of the Dirac constraint theory is elaborated up to the first order in the coupling constant. The Poincaré generators in the terms of particle variables are obtained. The relations between the instant form generators and front form ones are examined. The instant form Hamiltonian in the weak-relativistic approximation results in the Darwin Hamiltonian.

Interaction Dynamics of the External and Internal Degrees of Freedom of an Atom in the Resonant Field of a Standing Light Wave

The theory of the dynamic interaction of the external (translational) and internal (electronic) degrees of freedom of a two‐level atom in the field of a standing light wave in a perfect cavity of the Fabry–Perot type was developed. The theory describes the energy exchange between three subsystems, namely, translational, electronic, and field subsystems, as opposed to the theories of the parametric interaction (in the approximations of Raman–Nath and/or large resonance detuning) and of the atomic motion in free space. In the semiclassical approximation, the corresponding Heisenberg equations of motion were shown to form a closed Hamiltonian dynamic system with two degrees of freedom, namely, translational and collective electron–field degrees of freedom. This system is integrated in terms of the elliptic Jacobian functions in the resonance limit. The solutions obtained describe the effects of trapping of an atom in the periodic potential of the standing light wave, and its cooling and heating, as well as the effect of the dynamic Rabi oscillations. The latter is caused by the interaction of the internal and external atomic degrees of freedom through the radiation field.

Group approach to quantization of Yang-Mills theories: a cohomological origin of mass

New clues for the best understanding of the nature of the symmetry-breaking mechanism are revealed in this paper. A revision of the standard gauge transformation properties of Yang-Mills fields, according to a group approach to quantization scheme, enables the gauge group coordinates to acquire dynamical content outside the null mass shell. The corresponding extra (internal) field degrees of freedom are transferred to the vector potentials to conform massive vector bosons.

Dynamicalq-deformation in quantum theory and the stochastic limit

A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q depending on time. After the stochastic (or van Hove) limit, due to the nonlinearity, the atomic and field degrees of freedom become entangled in the sense that the field and the atomic variables no longer commute but give rise to a new algebra with new commutation relations replacing the Boson ones. This new algebra allows to give a simple proof of the fact that the non crossing half-planar diagrams give the dominating contribution in a weak coupling regime and to calculate explicitly the correlations associated to the new algebra. The above results depend crucially on the fact that we do not introduce any dipole or multipole approximation.

Two-particle systems in relativistic Schrödinger theory

The relativistic Schrodinger theory (RST) is applied to a general 2-particle system with electromagnetic interactions. The emphasis of the investigation lies on the exchange and overlap effects in connection with the development of adequate single-particle and 2-particle concepts. It is possible to eliminate the 2-particle quantities and to formulate the 2-particle theory exclusively in terms of single-particle quantities but then there arises a new unobservable field degree of freedom: `renormalization'.

Hamiltonian structure for classical electrodynamics of a point particle

We prove that, contrary to the common belief, the classical Maxwell electrodynamics of point-like particle may be formulated as an infinite dimensional Hamiltonian system. We derive a well defined quasi-local Hamiltonian which possesses direct physical interpretation being equal to the total energy of the composed system (field + particle). The phase space of this system is endowed with a very interesting symplectic structure. We prove that this structure is strongly nondegenerate and, therefore, enables one to define the consistent Poisson bracket for the particle and field degrees of freedom. We stress that this formulation is perfectly gauge invariant.

Homology and abelian lattice gauge theories

A simple Abelian model with both Higgs and gauge field degrees of freedom is investigated on a simplicial lattice of arbitrary dimension. We use group character expansion for both fields to get a diagrammatic expansion of the partition function. The diagrams consist of gauge group representation valued 1- and 2-chains. The diagrams are proved to satisfy the constraint that the boundary of the 2-chain representing the gauge field is equal to the 1-chain representing the Higgs field. Otherwise they identically vanish. Simple consequences of this are current conservation and the vanishing of non-null-homologous Wilson loops. Finally we use this picture for giving a lowest order estimate for the critical length of a string. This is the length at which the flux-tube string connecting two opposite charges is likely to break into two pieces due to pair creation.

Variational principle for electrodynamics of moving particles

A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles, proposed in [1], is now derived from a variational principle. For this purpose a new electrodynamical Lagrangian based on fluxes is constructed. As a result, we obtain the action principle where i) field degrees of freedom and particle degrees of freedom are kept at the same footing, ii) contrary to the standard formulation, no infinities arise, iii) energy (Hamiltonian) is obtained from the Lagrangian via the Legendre transformation, without any need of “adding a complete divergence”.

NONINTEGRABLE PHASE DYNAMICS IN TWO-DIMENSIONAL GAUGE MODELS

In two-dimensional gauge models the nonintegrable phases of the line Wilson integrals are the only physical gauge field degrees of freedom, providing the gauge field diminishes rather rapidly at spatial infinities. We construct a “physical” quantum Hamiltonian in terms of the physical degrees of freedom for the Schwinger model and the chiral Schwinger model. We show that in the latter case the physical quantum picture can be formulated in two equivalent ways: either in terms of the fermionic matter degrees of freedom moving in a linearly rising background electric field, or in terms of matter fields with exotic statistics.

Poincaré covariant particle dynamics. I. Intranuclear cascade model.

To analyze the high energy heavy ion reactions performed at Lawrence Berkeley BEVALAC, Brookhaven AGS, and CERN SPS we present a dynamical model that is entirely Poincar\'e covariant. The description of strong interactions by Lorentz-scalar quasipotentials makes possible a relativistic extension of the cascade concept without losing its inherent simplicity. No field degrees of freedom appear explicitly, neither in elastic nucleon scattering nor in particle creation processes. Although various formalisms describe directly interacting relativistic particles with identical solutions for the two-particle case, they all suffer from different problems in many-particle systems. The basis of our approach is a Hamiltonian formulation for N pointlike nucleons, moving unconstrained in an 8N-dimensional phase space. One additional Lorentz scalar is introduced for an appropriate parametrization of all trajectories, defining also the connection to the proper times of the individual interacting nucleons. The creation of particles, for which Hamiltonian dynamics does not provide a generic mechanism, is incorporated phenomenologically as a ``perturbative'' process. We describe heavy ion collisions as a sequence of two-particle reactions without any additional fit to experimental data. Pion yield and mass spectra of the heavy fragments agree reasonably well with BEVALAC results. We do not compare to experimental high energy data because the employed mechanism of particle production is certainly improper in that regime. However, the numerical results give an impression on how the reaction evolves.

Poincaré covariant particle dynamics. II. Fragmentation for ultrarelativistic reactions.

We present a Poincare covariant model for ultrarelativistic particle reactions without any field degrees of freedom. A relativistic two-particle interaction is made possible by an enlargement of phase space and a distinction between physical and canonical particle coordinates. A Hamiltonian formalism with a mass-like quasipotential defines the dynamics of the system. Then interaction at a distance causes a change of effective particle masses instead of energy. Particle production is incorporated by a phenomenological decay procedure for the constituents (partons) in a manner analogous to a string fragmentation mechanism. This pure particle picture for Poincare covariant collision dynamics (PCD model) is compared to other microscopic models and tested by simulations of [ital e][sup +][ital e][sup [minus]] jet events. Before application to more complex scenarios like ultrarelativistic heavy ion collisions, hard gluonic effects should be included. In the PCD model, this can be done by introduction of massive gluons as particles.

Cauchy problem for gauge field theories with external sources

The initial-value problem is studied for two models of gauge field theory in the presence of arbitrary external sources. The non-Abelian SU(2) Yang-Mills theory with a vanishing external charge J0a=0 allows for a clear distinction of the gauge field degrees of freedom into dynamical and non-dynamical ones. The case of general external sources Jmu a introduces new dynamical quantities-Lagrange multipliers Qa. Thus a modified Lagrangian has been taken as a starting point. A similar analysis is carried out for an Abelian model of scalar electrodynamics. In all three cases time evolution along classical equations of motion imposes no restriction on external sources and the dynamical degrees of freedom can take almost arbitrary initial values.

String field theory at finite temperature.

We present a real-time formalism enabling us to compute statistical averages of various quantum string field correlation functions and scattering amplitudes in the context of perturbation theory and functional methods. Second quantization of the string fields is carried out in the path-integral representation. Our finite-temperature formalism is a generalization of thermo field dynamics to string field theory for which a doubling of the physical string field degrees of freedom is required. Temperature formally enters our construction by imposing boundary conditions (Kubo-Martin-Schwinger condition) in the generating functional for the string field. Some explicit computations for the case of covariant open bosonic string theory are carried out.

On the origin of irreversibility in classical electrodynamic measurement processes

We present a new formalism for the microscopic classical electrodynamics of point charges in which the dynamic absence of self-interactions is enforced by the action principle, without eliminating the field degrees of freedom. In this context, free local radiation fields are dynamically prohibited. Instead radiation is carried by charge-field functionals of the current which have a negative parity under mathematical time reversal. This leads to the dynamic requirement of a physical time arrow in the equations of motion in order to preserve the overall mathphysical time-reversal symmetry of the formalism. Since this physical time arrow emerges electrodynamically without the need of external thermodynamic or cosmological criteria, it offers a dynamical explanation for the origin of irreversibility in classical electrodynamic measurement processes. “Science, like the arts, admits aesthetic criteria; it seeks theories that display ‘a proper conformity of the parts to one another and to the whole’ while still showing some strangeness in their proportion”—S. Chandrasekar.

A quantum field theory of dyons and photons

A relativistic quantum field theory is presented where point-like dyons describe closed spacetime trajectories and are coupled to e.m. field degrees of freedom, a path integral over trajectories and a functional integration over fields being performed. The formalism is manifestly Lorentz invariant since the field strengths rather than the e.m. potentials appear in the coupling. The Dirac-Schwinger quantization condition is a necessary assumption. We discuss some relevant features of the theory, e.g. a global U(1) symmetry redefining the dyons' charges and the particle content of the e.m. degrees of freedom.

A cluster expansion in field theory

A cluster expansion is proposed for the calculation of certain Green’s functions in field theory. The results presented are for λφ4 theory, expanded in the number of scalar closed loops through the introduction of the composite field, χ = i√λ/12 φ2. As an intermediate step, Feynman path integrals are used to perform the functional integration over the field degrees of freedom. The cluster expansion that results is equivalent to perturbation theory, but at lowest order sums up all the infrared behavior of the theory. Higher orders systematically include ultraviolet effects.

Semiclassical calculation of the photon propagator in two-dimensional scalar QED

This paper proposes a new semiclassical approach for calculating closed-loop quantities in scalar QED. This is carried through by the replacement of field degrees of freedom with particle coordinates, and then expanding about classical trajectories which dominate the theory. The one-charged-scalar closed-loop contribution to the photon propagator in two-dimensional scalar QED is calculated using this method. The semiclassical approximation developed gives the asymptotic behavior of the large-order terms in the perturbation expansion of the one-loop contribution to the photon self-energy.

Relativistic Correction to the Equilibrium Statistical Mechanics of a Dense Electron Gas

The grand partition function for a degenerate electron gas with relativistic corrections of order ${(\frac{v}{c})}^{2}$ in ring approximation is given. The technique used is the method of Montroll and Ward; in this problem independent field degrees of freedom are not required. The correlation energy, which represents a generalization of the Gell-Mann-Brueckner result, is obtained. Comparison with the field-theoretic results of Akhiezer and Peletminskii is made, with the same results. However, in view of the absence of independent field degrees of freedom in our treatment, renormalization is not required here (to obtain their result Akhiezer and Peletminskii must resort to charge, mass, and vacuum renormalization).