Partial measurement in the Bohm-Bub hidden-variable theory

The Bohm-Bub hidden-variable theory is able to predict the results of measuring a quantum system only in the special case where the set of commuting observables being measured is complete. To handle the much more common case where the set is incomplete, Tutsch has proposed a generalization of the Bohm-Bub model. Unfortunately, as we show here, Tutsch's original method does not yield the correct quantum mechanical transition probabilities. On the other hand, Belinfante's modification of Tutsch's method does yield the correct probabilities, and it gives a satisfactory hidden-variable theory of partial measurement for the case where one or more commuting variable(s) are measured at a single space-time point. In the case where the variables are measured at different space-time points, the theory is inadequate, due to the fact that it is not relativistically covariant, and does not take relaxation of the hidden variables into account.     

Relativistically covariant calculation of hyperon formfactors

Electroweak formfactors are calculated using a Lorentz invariant formalism based on boosted bag-model. The Lorentz-invariance is explicitly demonstrated. Only one version of the formalism can be consistent with the conserved vector current (CVC) constraint. Some connections with the quasi-potential formalism are discussed. Difficulties encountered in the usage of the chiral-bag model are described. The results are compared with the earlier bag model calculations for semileptonic weak decays.     

Relativistically covariant chronological ordering of interaction lagrangians

A general form of chronological ordering is proposed, based on introduction of relativistically invariant multipoint step functions (x₁, ..., x_n). A system of recursive relations is established for these functions, which guarantees that the scattering matrix is unitary, covariant, and causal. The explicit form of the first four -functions is found. A comparative analysis of the known methods of chronological ordering is given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 70–73, May, 1990.     

A first-order equation for spin in a manifestly relativistically covariant quantum theory

Relativistic quantum mechanics has been formulated as a theory of the evolution ofevents in spacetime; the wave functions are square-integrable functions on the four-dimensional spacetime, parametrized by a universal invariant world time . The representation of states with spin is induced with a little group that is the subgroup of O(3, 1) leaving invariant a timelike vector n; a positive definite invariant scalar product, for which matrix elements of tensor operators are covariant, emerges from this construction. In a previous study a second-order equation was introduced similar to the second-order Dirac equation, based on a quadratic function of two operators which are the self-adjoint parts, in this new scalar product, of p. It is shown in this paper that one of these operators, in fact the one from which the gyromagnetic moment is obtained, can be used to construct a first-order equation. The corresponding quantum theory is somewhat analogous to Dirac's spinor form; the Hamilton equations appear to describe dynamical degrees of freedom in a spacelike hyperplane orthogonal to n (in Dirac's theory the motion appears to be lightlike). It is shown that the integration over n required by unitarity results in timelike motion (as in the expectation value of Dirac's ). Explicit forms are obtained for the wave functions and currents for free motion. The general form of the theory is written for the (five-dimensional) pre-Maxwell fields required by gauge invariance.     

Tunneling measurement of a single quantum spin

Measurement of the tunneling current of spin-polarized electrons via a molecule with a localized spin provides information on the orientation of that spin. We show that a strong tunneling current due to the shot noise suppresses the spin dynamics, such as the spin precession in an external magnetic field, and the relaxation due to the environment (quantum Zeno effect). A weak tunneling current preserves the spin precession with the oscillatory component of the current of the same order as the noise. We propose an experiment to observe the Zeno effect in a tunneling system and describe how the tunneling current may be used to read a qubit represented by a single spin 1/2.     

A theory of electromagnetism with uniquely defined potential and covariant conserved spin

The Lagrangian ½? ₀ c ² ? _µ A _ν ? ^µ A ^ν is shown to yield a non-gauge-invariant theory of electromagnetism. The potential is uniquely determined by the inhomogeneous wave equation and boundary conditions at infinity. The Lorenz condition and minimal coupling follow from charge conservation. Electromagnetic spin is conserved and a spin operator is proposed without sacrificing covariance. Covariant quantisation is carried out without redefining the metric. It is a valid alternative to the standard approach since it makes the same experimental predictions.     

Construction of a covariant spinor field theory

A covariant theory is constructed of a spinor field in a space which is represented by the local topological product of a space X_n and a space of values of a geometrical object η. The covariant nonlinear spinor field theory constructed preserves the principles of the theory of the unified field and is compatible with the theory of gauge fields.     

A spin observable for a Dirac particle

We discuss the form of the spin operator in relativistic quantum mechanics. We derive the form of the spin operator in the case when the states with negative energies are admitted. It appears that for a Dirac particle the spin operator reduces to the so called mean-spin operator introduced by Foldy and Wouthuysen. We show that the spin operator transforms under Lorentz group action according to an operator Wigner rotation, analogously as a Bloch vector describing polarization of a particle in momentum representation.     

Three-loop corrections in a covariant effective field theory

Chiral effective field theories have been used with success in the study of nuclear structure. It is of interest to systematically improve these energy functionals (particularly that of quantum hadrodynamics) through the inclusion of many-body correlations. One possible source of improvement is the loop expansion. Using the techniques of Infrared Regularization, the short-range, local dynamics at each order in the loops is absorbed into the parameterization of the underlying effective Lagrangian. The remaining nonlocal, exchange correlations must be calculated explicitly. Given that the interactions of quantum hadrodynamics are relatively soft, the loop expansion may be manageable or even perturbative in nuclear matter. This work investigates the role played by the three-loop contributions to the loop expansion for quantum hadrodynamics.     

Feynman propagator for a particle with arbitrary spin

Based on the solution to the Rarita-Schwinger equations, a direct derivation of the projection operator and propagator for a particle with arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin; the general commutation rules and Feynman propagator for a free particle of any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, 4 are provided.Received: 13 March 2003, Revised: 24 April 2005, Published online: 6 July 2005     

Projective measurement of a single nuclear spin qubit by using two-mode cavity QED

We report the implementation of projective measurement on a single 1/2 nuclear spin of the (171)Yb atom by measuring the polarization of cavity-enhanced fluorescence. To obtain cavity-enhanced fluorescence having a nuclear-spin-dependent polarization, we construct a two-mode cavity QED system, in which two cyclic transitions are independently coupled to each of the orthogonally polarized cavity modes, by manipulating the energy level of (171)Yb. This system can associate the nuclear spin degrees of freedom with the polarization of photons, which will facilitate the development of hybrid quantum systems.     

A proposal for covariant renormalizable field theory of gravity

The class of covariant gravity theories which have nice ultraviolet behavior and seem to be (super)-renormalizable is proposed. The apparent breaking of Lorentz invariance occurs due to the coupling with the effective fluid which is induced by Lagrange multiplier constrained scalar field. Spatially-flat FRW cosmology for such covariant field gravity may have accelerating solutions. Renormalizable versions of more complicated modified gravity which depends on Riemann and Ricci tensor squared may be constructed in the same way.     

A contribution to the theory of the pauli-fierz equation for a particle with spin 3/2

Commutation rules for the Pauli-Fierz equation are given in the parametric form. The Hamiltonian and subsidiary conditions for a free particle are derived. The two subsidiary conditions are in a form which expresses that an operator and its time derivative applied to the wave function give zero. The practical applicability of the formalism of parametric commutation rules for special computations is verified by an example of the magnetic moment.     

Bell's inequality for a single particle

Bell's inequality must be satisfied by a theory that can be based on local realistic variables. We derive such an inequality and show that it is violated by some quantum mechanical states. These states may be looked upon as pertaining to one particle.This paper is a contribution in honor of Prof. M. Jammer's 80th birthday April 13, 1995.     

Variational formulation of covariant eikonal theory for vector waves

The eikonal theory of wave propagation is developed by means of a Lorentz-covariant variational principle, involving functions defined on the natural eight-dimensional phase space of rays. The wave field is a four-vector representing the electromagnetic potential, while the medium is represented by an anisotropic, dispersive nonuniform dielectric tensor D^μν(k,x). The eikonal expansion yields, to lowest order, the hamiltonian ray equations, which define the lagrangian manifold k(x), and the wave-action conservation law, which determines the wave-amplitude transport along the rays. The first-order contribution to the variational principle yields a concise expression for the transport of the polarization phase. The symmetry between k-space and x-space allows for a simple implementation of the Maslov transform, which avoids the difficulties of caustic singularities.     

Magnetic properties of antiferromagnetic quantum Heisenberg spin systems with a strict single particle site occupation

We work out the magnetization and susceptibility of Heisenberg- and XXZ-model antiferromagnet spin-1/2 systems in D dimensions under a rigorous constraint of single particle site occupancy. Quantum and thermal fluctuations are taken into account up to the first order in a loop expansion beyond the Néel state mean field solution. We discuss the results, their validity in the vicinity of the critical point and compare them with the results obtained by means of a spin wave approach.