Proposed test for a hidden variables theory

A hidden variables model for quantum mechanics is proposed and a possible test for its validity is described.     

Angular correlation of scattered annihilation photons, to test the possibility of hidden variables in quantum theory

Angular correlations of the annihilation photons, Compton scattered by plastic scintillators and detected by means of NaI (T1) crystals, have been measured in order to test the possibility of deviations of the experimental results from the predictions of the quantum theory. In fact, Jauch and Bohm, starting with different motivations, both arrive at the possibility of a lower correlation ratio between the two orthogonal polarization states of the two photons than predicted by quantum theory. This in turn should give a lower azimuthal anisotropy in the angular correlations. Our experimental results compared with the theoretical predictions, after correction for finite geometry by means of a Montecarlo method, do not confirm quantum theory and exclude the hypotheses of Jauch and of Bohm. We are continuing the experiment in order to test wether the breakdown in the polarization correlation depends on the distance (spatial and/or temporal) between the two correlated scattering events, as suggested by Jauch. Paper A 34 presented at 3 rd Internat'l Conf. Positron Annihilation, Otaniemi, Finland (August 1973).     

Symmetry breaking and measurement theory

For studying the problem of measurement we accept the statistical interpretation of quantum mechanics, but we take into account, that in a sequence of measurements, offdiagonal terms arise which cannot obviously be interpreted as the probability of a sequence of macroscopic events. We demonstrate, however, their vanishing for ordinary measurement processes by observing that the measurement apparatus undergoes a symmetry breaking transition during the measurement.1. On leave from the Central Research Institute for Physics, Budapest, Hungary.     

Multimomentum hamiltonian formalism in quantum field theory

The familiar generating functional in quantum field theory fail to be true measures and make sense only in framework of perturbation theory. In our approach, generating functionals are defined strictly as the Fourier transforms of Gaussian measures in nuclear spaces of multimomentum canonical variables when field momenta correspond to derivatives of fields with respect to all world coordinates, not only to time.     

Gauge-invariant bilocal formalism in quantum field theory

A gauge-invariant continuation of the S-matrix generating functional outside the mass shell is proposed. A generating functional of gauge-invariant Green functions is obtained. Using the path integral formalism, collective gauge-invariant bilocal field variables are introduced. With the aid of the bilocal formalism, an integral equation is obtained for the gauge-invariant spinor propagator. It is shown that the propagator of the bilocal field corresponds to the gauge-invariant wave function of a two-particle system in ladder approximation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 105–111, April, 1990.The authors thank A. N. Sisakyan, N. B. Skachkov, and O. Yu. Shevchenko for their interest to this work and useful discussions of the obtained results.     

Symmetry at the foundations of quantum theory

The symmetry implications of the postulates of quantum theory are investigated.On leave from School of Physics and Astronomy, Tel-Aviv University, 69978 Tel-Aviv, Israel.     

Symmetry theory in a two-level quantum system

We develop the theory of symmetry for a two-level quantum system in oder to illustrate the main ideas of the general theory of symmetry in quantum theory. It is based on the diffeomorphism of the two-dimensional sphere S ² onto the space of states P ¹ and the isomorphism between the groups P(2) and SO ₃ (). In particular, rotational invariance leads to the appearance of the spin1/2 in a natural way.     

Nonlinear quantum mechanics,the superposition principle,and the quantum measurement problem

There are four reasons why our present knowledge and understanding of quantum mechanics can be regarded as incomplete. (1) The principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. (2) There is no universally agreed upon explanation for the process of quantum measurement. (3) There is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. (4) Most importantly, the concept of time is classical and hence external to quantum mechanics: there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the aforesaid problems. We use a physically motivated model for a nonlinear Schr?dinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects (lifetime is too small). It also suggests that ongoing laboratory experiments may be able to detect the finite superposition lifetime for mesoscopic objects in the near future.     

State-dependent dynamical variables in quantum theory

State-dependent local dynamical variables (LDVs) sharply differ from the ordinary operators of quantum mechanics. The N-level model system shows the physical importance of such operators in the complex projective Hilbert state space CP(N?1). The process of quantum measurement in terms of LDVs is described.     

Legendre transforms and r-particle irreducibility in quantum field theory: The formalism for r = 1, 2

We analyze the first and second Legendre transforms Γ^(r) (r = 1, 2) of the generating functional G for connected Green's functions in Euclidean boson field theories. By using Spencer's idea of t-lines we define and prove irreducibility properties independently of perturbation theory. In particular we prove that Γ^(r) generates r-irreducible vertex functions, r-irreducible expectations and r-field projectors; moreover, Γ⁽²⁾ generates (generalized) Bethe-Salpeter kernels with 2-cluster-irreducibility properties.     

Symmetry as a source of hidden coherent structures in quantum physics: General outlook and examples

A general algebraic approach incorporating both invariance groups and dynamical symmetry algebras is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum manybody physics models due to symmetries of their Hamiltonians H. Its general ideas are manifested on some recent new examples: (1) G-invariant biphotons and a related SU(2)-invariant treatment of unpolarized light; (2) quasispin clusters in nonlinear models of quantum optics; and (3) construction of composite particles and (para)fields from G-invariant clusters due to internal symmetries.     

Physical principles in quantum field theory and in covariant harmonic oscillator formalism

It is shown that both covariant harmonic oscillator formalism and quantum field theory are based on common physical principles which include Poincaré covariance, Heisenberg's space-momentum uncertainty relation, and Dirac's “C-number” time-energy uncertainty relation. It is shown in particular that the oscillator wave functions are derivable from the physical principles which are used in the derivation of the Klein-Nishina formula.     

Problems of the quantum theory of measurement

After a short review of the present situation of the quantum theory of measurement, a formulation of the measuring process is given, which allows an “objective” interpretation. Starting from the unitary time transformation of the states of the measured systemS and the measuring deviceM, it is shown that after appropriate specification of the interaction HamiltonianH _int betweenS andM and the macroscopic structure ofM, the statistical operatorW ofS+M approximately develops into the mixture, which is desired as result of the measuring process. During the process the interference terms practically vanish in the sense of weak operator convergence, while on the other hand their Hilbert-Schmidt norm remains constant.