Semiclassical Field Theory Research Articles

PHANTOM UNIVERSE FROM CPT SYMMETRIC QFT

We develop a generalization of semiclassical field theory for the case of non-Hermitian Hamiltonians with CPT symmetry and construct a classical cosmological, scalar-field based model describing a smooth transition from ordinary dark energy to the phantom one. Our model arises from a Lagrangian with a complex potential leading to a non-trivial vacuum with real vacuum energy. Equivalence with models involving two scalar fields one of which is phantom-like is discussed.

Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator

Having in mind applications to gravitational wave theory (in connection with the radiation reaction problem), stochastic semiclassical gravity (in connection with the regularization of the noise kernel) and quantum field theory in higher-dimensional curved spacetime (in connection with the Hadamard regularization of the stress-energy tensor), we improve the DeWitt-Schwinger and Hadamard representations of the Feynman propagator of a massive scalar field theory defined on an arbitrary gravitational background by deriving higher-order terms for the covariant Taylor series expansions of the geometrical coefficients -- i.e., the DeWitt and Hadamard coefficients -- that define them.

Relativistically Covariant Quantum Field Theory of the Maslov Complex Germ

We consider an explicitly covariant formulation of the quantum field theory of the Maslov complex germ (semiclassical field theory) in the example of a scalar field. The main object in the theory is the “semiclassical bundle” whose base is the set of classical states and whose fibers are the spaces of states of the quantum theory in an external field. The respective semiclassical states occurring in the Maslov complex germ theory at a point and in the theory of Lagrangian manifolds with a complex germ are represented by points and surfaces in the semiclassical bundle space. We formulate semiclassical analogues of quantum field theory axioms and establish a relation between the covariant semiclassical theory and both the Hamiltonian formulation previously constructed and the axiomatic field theory constructions Schwinger sources, the Bogoliubov S-matrix, and the Lehmann-Symanzik-Zimmermann R-functions. We propose a new covariant formulation of classical field theory and a scheme of semiclassical quantization of fields that does not involve a postulated replacement of Poisson brackets with commutators.

Influence of Tunneling on Electron Screening in Low Energy Nuclear Reactions

Using a semiclassical mean field theory, we show that the screening potential exhibits a characteristic radial variation in the tunneling region in sharp contrast to the assumption of the constant shift in all previous works. Also, we show that the explicit treatment of the tunneling region gives a larger screening energy than that in the conventional approach, which studies the time evolution only in the classical region and estimates the screening energy from the screening potential at the external classical turning point. This modification becomes important if the electronic state is not a single adiabatic state at the external turning point. Furthermore, as an alternative solution of the screening problem, we give the estimation for the effect of extra electrons which are caught into the ground state of the projectile by using constraint molecular dynamics.

Influence of tunneling on electron screening in low energy nuclear reactions in laboratories

Using a semiclassical mean field theory, we show that the screening potential exhibits a characteristic radial variation in the tunneling region in sharp contrast to the assumption of the constant shift in all previous works. Also, we show that the explicit treatment of the tunneling region gives a larger screening energy than that in the conventional approach, which studies the time evolution only in the classical region and estimates the screening energy from the screening potential at the external classical turning point. This modification becomes important if the electronic state is not a single adiabatic state at the external turning point either by pre-tunneling transitions of the electronic state or by the symmetry of the system even if there is no essential change with the electronic state in the tunneling region.

Screening Effects in Low Energy Nuclear Reactions in Laboratories

Nuclear reactions in stars are known to be affected by the surrounding plasma. The reaction rates between various light nuclei measured in recent laboratory experiments show an increasing enhancement with decreasing collision energy compared with the extrapolation from higher energies. This phenomenon has been analysed in terms of the screening effects by bound target electrons. Surprisingly in all systems experimentally studied so far the extracted screening energy is significantly larger than the value in the adiabatic limit, which is expected to be the maximum value. Comparison with the recent indirect mothod named the Trojan Horse method also suggests a large screening effect to exist in direct measurements. We review the present status of the theoretical and experimental studies of this problem, and touch a recent study which has pointed out the importance of the explicit treatment of the behaviour of electrons in the tunneling region based on a semiclassical mean field theory of quantum tunneling.

S-duality of the Leigh-Strassler Deformation via Matrix Models

We investigate an exactly marginal N=1 supersymmetric deformation of SU(N) N=4 supersymmetric Yang-Mills theory discovered by Leigh and Strassler. We use a matrix model to compute the exact superpotential for a further massive deformation of the U(N) Leigh-Strassler theory. We then show how the exact superpotential and eigenvalue spectrum for the SU(N) theory follows by a process of integrating-in. We find that different vacua are related by an action of the SL(2,Z) modular group on the bare couplings of the theory extending the action of electric-magnetic duality away from the N=4 theory. We perform non-trivial tests of the matrix model results against semiclassical field theory analysis. We also show that there are interesting points in parameter space where condensates can diverge and vacua disappear. Based on the matrix model results, we propose an exact elliptic superpotential to describe the theory compactified on a circle of finite radius.

Renormalization of Poincaré transformations in Hamiltonian semiclassical field theory

Semiclassical Hamiltonian field theory is investigated from the axiomatic point of view. A notion of a semiclassical state is introduced. An “elementary” semiclassical state is specified by a set of classical field configurations and quantum states in this external field. “Composed” semiclassical states viewed as formal superpositions of “elementary” states are nontrivial only if the Maslov isotropic condition is satisfied; the inner product of “composed” semiclassical states is degenerate. The mathematical proof of Poincaré invariance of semiclassical field theory is obtained for “elementary” and “composed” semiclassical states. The notion of semiclassical field is introduced; its Poincaré invariance is also mathematically proved.

Recent developments in nuclear theory

Two recent developments are reviewed. (1) The Pairing-Plus-Quadrupole model has recently been extended to medium-weight nuclei with A=108–134. (2) The semiclassical unified field theory of fundamental forces has been developed.

Semiclassical Symmetries

Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are considered. An infinitesimal analog of group relation is written. Sufficient conditions for reconstructing semiclassical group transformations (integrability of representation of Lie algebra) are discussed. The obtained results may be used for mathematical proof of Poincare invariance of semiclassical Hamiltonian field theory and for investigation of quantum anomalies.

Semiclassical Mean Field Theory of Quantum Tunneling in a Coupled System

Semiclassical Mean Field Theory of Quantum Tunneling in a Coupled System

Semiclassical field theory approach to quantum chaos

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the form of a functional supermatrix non-linear σ-model where the effective action involves the evolution operator of the classical dynamics. Low-lying degrees of freedom of the field theory are shown to reflect the irreversible classical dynamics describing relaxation of phase space distributions. The validity of this approach is investigated over a wide range of energy scales. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach accounts correctly for the short-time limit yielding results which agree with the diagonal approximation of periodic orbit theory.

Quantum chaos, irreversible classical dynamics, and random matrix theory.

The Bohigas-Giannoni-Schmit conjecture stating that the statistical spectral properties of systems which are chaotic in their classical limit coincide with random matrix theory (RMT) is proved. A new semiclassical field theory for individual chaotic systems is constructed in the framework of a nonlinear $\ensuremath{\sigma}$ model. The low lying modes are shown to be associated with the Perron-Frobenius (PF) spectrum of the underlying irreversible classical dynamics. It is shown that the existence of a gap in the PF spectrum results in RMT behavior. Moreover, our formalism offers a way of calculating system specific corrections beyond RMT.

Semiclassical meson-baryon dynamics from large- Nc QCD

The large- N c limit of the meson-baryon effective Lagrangian is shown to reduce to a semiclassical field theory. A chiral bag structure emerges naturally in the N c → ∞ limit. A possible connection between the chiral bag picture and the Skyrme model is discussed. The classical meson-baryon theory is used to reproduce the M π 3 non-analytic correction to the baryon mass obtained previously as a loop correction in chiral perturbation theory.

Topological “observables” in semiclassical field theories

We give a geometrical set-up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces M. The standard examples are of course Yang-Mills theory and non-linear σ-models. The relevant space here is a family of measure spaces N ̃ →M , with standard fibre a distribution space, given by a suitable extension of the normal bundle to M in the space of the smooth fields. Over N ̃ there is a probability measure dμ given by the twisted product of the (normalized) volume element on M and the family of gaussian measures with covariance given by the tree propagator C φ in the background of an instanton φϵM. The space of “observables”, i.e., measurable functions on ( N ̃ , dμ ), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on M. The expectation value of these topological “observables” does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.

Violations of a simple inequality for classical fields.

It has been shown that two correlated photons incident upon two distant interrerometers can give a coincidence counting rate that depends nonlocally on the sum or the phases or the two interrerometers. It is shown here that the results or existing experiments violate a simple inequality that must be satisfied by any classical or semiclassical field theory. The inequality provides a graphic illustration or the lack or objective realism or the electric field

Approximate inversion method for obtaining polyatomic potential energy surfaces from ro-vibrational spectra

The extension to polyatomic molecules of the RKR procedure for inversion of ro-vibrational spectra to deduce the intramolecular potential surface depends on solving the semiclassical quantization problem for coupled modes. The semiclassical self-consistent field theory (SC-SCF) proposed recently provides an approximate method for solving the coupled mode problem, and thereby provides a means to extend RKR. We derive a closed-form, convenient expression for the inversion transform that constructs directly the potential surface from the spectral data. The inversion should be valid in the region (well below the quasi-continuum) for which SC-SCF holds. We test the method for a model problem of two coupled modes, and find that it works very well. For practical inversions, difficulties in assignment or in obtaining the requisite number of frequencies might occur; nevertheless, the extended RKR is direct, non-iterative, and potentially useful.

Renormalization of semiclassical field theories

We discuss a simple model which shares some of the essential features of the semiclassical theory of gravitation. In this model, a classical scalar field υ interacts with a quantized field φ̌. We describe a consistent and unambiguous renormalization scheme for the model.

Theory of a free electron laser

Radiation from electrons traveling through a static transverse periodic magnetic field is studied using classical, semiclassical, and quantum field theories. Stimulated emission rates and laser evolution equations describing exponential gain and saturation are derived from basic principles.