The CPT-theorem in two-dimensional theories of local observables

Let be a von Neumann algebra with cyclic and separating vector , and letU(a) be a continuous unitary representation ofR with positive generator and as fixed point. If these unitaries induce for positive arguments endomorphisms of then the modular group act as dilatations on the group of unitaries. Using this it will be shown that every theory of local observables in two dimensions, which is covariant under translation only, can be imbedded into a theory of local observables covariant under the whole Poincaré group. This theory is also covariant under the CPT-transformation.     

On the connection between spin glasses and gauge field theories

A simple connection between Ising spin glasses and the Z₂ lattice gauge theory, at negative plaquette temperatures, is presented. It is first shown that annealed models give useful lower bounds on the free energy and ground-state energy of spin glasses. However, they have unphysical low temperature properties (e.g. a negative entropy), which are related to a temperature dependence of the frustration. A restricted annealing scheme is presented which remedies this deficiency through the introduction of a pure gauge coupling counterterm. The possible phase diagrams of the lattice gauge system and their relevance to spin glass transitions are discussed.     

The energy-momentum spectrum in local field theories with broken Lorentz-symmetry

Assuming locality of the observables and positivity of the energy it is shown that the joint spectrum of the energy-momentum operators has a Lorentz-invariant lower boundary in all superselection sectors. This result is of interest if the Lorentz-symmetry is (spontaneously) broken, such as in the charged sectors of quantum electrodynamics.     

Remarks on the connection between conventional reaction theories and the integral-equation approach to few-particle scattering

The method of exact integral equations is formulated in terms of wavefunctions in such a way that a direct comparision becomes possible to the more conventional methods for treating nuclear reactions. It is shown how to develop the wavefunction rigorously in an expansion which outside the reaction region is identical to the resonating-group ansatz (below the breakup threshold). Common and different aspects of the approximations employed in both approaches are clarified. The three-particle problem is used for the purpose of demonstration and for the execution of test calculations. Possibilities are discussed of how experience with one approach could be fruitful for the further development of the other.     

General semi-classical method for collective motion and its connection with the Rowe-Basserman and marumori theories,and adiabatic limits

In recent work, we have shown that in the adiabatic limit (large amplitude, small momentum), time-dependent Hartree-Fock theory (TDHF) yields a well-defined theory of large-amplitude collective motion which provides an essentially unique construction for a collective hamiltonian. An alternative theory, put forward by Rowe and Basserman and by Marumori is, apparently, not restricted to small momenta. We describe a general framework for the study of collective motion in the semi-classical limit without limitation on the size of coordinates or momenta, which includes all previous methods as limiting cases. We find it convenient, as in the past, to consider two general systems: first, a system with n degrees of freedom and no special permutation symmetry, and, second, a system of fermions described in TDHF. For both systems the problem can be formulated as a search for a hamiltonian flow confined to a finite-dimensional hypersurface in a phase space, which itself may be finite- or infinite-dimensional. Though, in general, there are no exact solutions to this problem, we can formulate consistent approximation schemes corresponding to both the adiabatic and Rowe-Basserman, and Marumori limits. We also show how to extend the momentum expansion, which underlies the adiabatic approximation, to higher orders in the momentum. We thereby confirm the structure of the theory found in our previous work.     

Objective local theories and the symmetry between analyzers

It is shown that a necessary condition for objective local theories to be equivalent to quantum mechanics in correlation experiments in the existence of a dissymmetry between analyzers or, alternately, a space anisotropy. No supplementary assumption is made about detection probabilities when the variables of the local theory all lie in the plane of the analyzers. The proof extends to three-dimensional variables if one supposes the detection process to be free of instabilities.     

The incompatibility between local hidden variable theories and the fundamental conservation laws

I discuss in detail the result that the Bell’s inequalities derived in the context of local hidden variable theories for discrete quantized observables can be satisfied only if a fundamental conservation law is violated on the average. This result shows that such theories are physically nonviable, and makes the demarcating criteria of the Bell’s inequalities redundant. I show that a unique correlation function can be derived from the validity of the conservation law alone and this coincides with the quantum mechanical correlation function. Thus, any theory with a different correlation function, like any local hidden variable theory, is incompatible with the fundamental conservation laws and space-time symmetries. The results are discussed in the context of two-particle singlet and triplet states, GHZ states, and two-particle double slit interferometry. Some observations on quantum entropy, entanglement, and nonlocality are also discussed.     

The internal symmetry group of a connection on a principal fiber bundle with applications to gauge field theories

The internal symmetry group of a connection on a principal fiber bundleP is studied. It is shown that this group is a smooth proper Lie transformation group ofP, which, ifP is connected, is also free. Moreover, this group is shown to be isomorphic to the centralizer of the holonomy group of the connection. Several examples and applications of these results to gauge field theories are given.     

The compatibility between quantum mechanics and local realist theories in atomic cascade experiments

We show that the divergence between the predictions of quantum optics and the local realist theory known as stochastic optics, for the extended type of photon-coincidence experiment described recently by de Caro, is of the same order of magnitude as for Aspect-type experiments. This means that, in such new experiments, as in those so far performed, counting statistics will have to be greatly improved before a discrimination between the two theories becomes possible.We also show that the outstanding difference between the two theories is that, while stochastic optics uses a genuine, that is, positive, detection probability, the corresponding quantum formalism leads to a pseudoprobability. Nevertheless, there is a striking parallel, in that both theories recognize the phenomenon known as enhancement, and both describe it as having its origin in a mixing of the signal field with the zero-point field by a polarizing device.     

The local quantized superfield,CPT, and the connection between spin and statistics

Starting from the principles of the local quantized ordinary fields in four dimensions the theory is constructed for the local quantized superfield. From the normal connection between between spin and statistics of ordinary fields the local commutativity (anticommutativity) for superfields is obtained. Also the CPT invariance of Wightman's superfunction and the general theorem on the connection between spin and statistics are proved.     

Microscopic diagonal entropy and its connection to basic thermodynamic relations

We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as S_d=-∑_nρ_nnlnρ_nn with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy S_n = −Trρ ln ρ. However, in contrast to S_n, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed through the energy distribution function and thus it is measurable, at least in principle. Under very generic assumptions of the locality of the Hamiltonian and non-integrability the d-entropy becomes a unique function of the average energy in large systems and automatically satisfies the fundamental thermodynamic relation. This relation reduces to the first law of thermodynamics for quasi-static processes. The d-entropy is also automatically conserved for adiabatic processes. We illustrate our results with explicit examples and show that S_d behaves consistently with expectations from thermodynamics.     

Symmetric extensions of quantum States and local hidden variable theories

While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and nonlocality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the problem of constructing local hidden variable theories for quantum states. The method is based on constructing a so-called symmetric quasiextension of the quantum state that gives rise to a local hidden variable model with a certain number of settings for the observers Alice and Bob.     

The inaction approach to gauge theories

The inaction approach introduced previously for φ⁴ [1] is generalized to gauge theories. It combines the advantages of the effective field theory and causal approaches to quantum fields. Also, it suggests ways to generalizing gauge theories.     

A five-dimensional Dirac-theory and its relation to nonlocal theories in four dimensions

A generalization of the Dirac-theory to one time- and four space-like coordinates is discussed. The consequences of discretizing the fifth dimension are studied and a relationship with nonlocal four dimensional field-theory is found.