Showing papers on "Quantization (physics) published in 1970"

An Introduction to Field Quantization

Abstract: An introduction to field quantization , An introduction to field quantization , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Formal Description of Measurements in Local Quantum Field Theory

Abstract: Ideal measurements in quantum mechanics can be described formally as instantaneous changes of the state vector or, more generally, of the density matrix $W$. By its lack of covariance, this formalism is not very adequate for relativistic quantum theories such as local field theory. For the latter, we propose a modified formalism, according to which a field measurement in a space-time region $C$ changes the field state $W$ in the future and side cone of $C$. This proposal is justified by physical considerations.

Foundations for Quantum Mechanics

Abstract: A discussion is given of the structure of a physical theory and an ``ideal form'' for such a theory is proposed. The essential feature is that all concepts should be defined in operational terms. Quantum (and classical) mechanics is then formulated in this way (the formulation being, however, restricted to the kinematical theory). This requires the introduction of the concept of a mixed test, related to a pure test (or ``question'') just as a mixed state is related to a pure state. In the new formulation, the primitive concepts are not states and observables but certain operationally accessible mixed states and tests called physical. The notion of a C*‐system is introduced; each such system is characterized by a certain C*‐algebra. The structure of a general C*‐system is then studied, all concepts being defined in terms of physical states and tests. It is shown first how pure states and tests can be so defined. The quantum analog of the phase space of classical mechanics is then constructed and on it is built a mathematical structure, called a q‐topology, which is a quantum analog of the topology of classical phase space. Mathematically, a q‐topology is related to a noncommutative C*‐algebra as an ordinary topology is related to a commutative C*‐algebra. Some properties of the q‐topology of a C*‐system are given. An appendix contains some physically motivated examples illustrating the theory.

Quantum mechanical calculation of the carrier distribution and the thickness of the inversion layer of a MOS field-effect transistor

Abstract: The carrier distribution in the inversion layer of a MOS-structure at room temperature was calculated assuming a quantization of the allowed energy levels at the surface and a linear electrostatic potential. It was found that for strong inversion the carrier distribution deviates considerably from the one found by using classical statistics but approaches the classical limit for weak inversion when many electric subbands are occupied. A new definition for the channel thickness was introduced based on the integrated charge in the channel and compared to other definitions. Channel thicknesses so defined range from 30 to 400 A for practical devices depending on surface potential. The integrated charge in the channel deviated little from the one found using classical statistics.

Ultralocal scalar field models.

Abstract: In this paper the quantum theory of ultralocal scalar fields is developed Such fields are distinguished by the independent temporal development of the field at each spacial point Although the classical theories fit into the canonical framework, this is not the case for the quantum theories (with the exception of the free field) Explicit operator constructions are given for the field and the Hamiltonian as well as several other operators, and the calculation of the truncated vacuum expectation values is reduced to an associated single degree of freedom calculation It is shown that construction of the Hamiltonian from the field, as well as the transition from the interaction to the noninteracting theories entails various infinite renormalizations which are made explicit

Charge quantization, compactness of the gauge group, and flux quantization

Abstract: The relationship between charge quantization and the compactness of the gauge group is discussed. Also, remarks are made about charge quantization and the observation of flux quantization in superconductors.

Quantization of general relativity

Abstract: Several theories of quantum general relativity have been formulated. Each of these theories has elements of arbitrariness and ambiguity as well as technical difficulty which make it less than satisfactory. However, the construction of these theories has revealed much about the structure of general relativity as a dynamical system and has spurred the development of new approaches to quantum theory. Canonical, sum-over-histories and source theory approaches to the quantization of the gravitational field in the absence of matter are reviewed in terms of a unified notation. Discussions of quantum theory and general relativity are provided to make the review self-contained for readers with a general physics background. The quantization of open space-time geometries (graviton scattering) is treated in sufficient detail to reveal the basic mathematical structure of the formalism. The quantization of closed universes (quantum cosmology) is discussed with particular attention to the superspace concept and the construction of finite-dimensional model quantum theories. Superspace, the domain manifold of the quantum state functional in general relativity, is also discussed separately.

Aharonov-Bohm Effect—Quantum Effects on Charged Particles in Field-Free Regions

Abstract: The Aharonov-Bohm effect is relatively little known, but it poses fundamental questions in quantum theory. It concerns physical effects on charged particles in field-free regions. The present paper provides an over-all critical review and commentary on the literature of the Aharonov-Bohm effect. The two fundamental questions raised by the effect concern the role of the force concept in quantum mechanics, and the localizability of physical effects principle. A recent letter from Professor Bohm concerning his evaluation of the significance of the effect is included in the Appendix.

A Superposition Principle in Physics

Abstract: A superposition principle is considered both in classical mechanics and in the quantum logic approach to quantum mechanics. It is shown, roughly speaking, that in classical mechanics the only type of superposition of states is a mixture and that no pure state is a nontrivial superposition of other pure states. In quantum mechanics it is shown that, if a superposition principle holds, then the quantum logic is a complete atomic lattice.

Gauge Problem in Quantum Field Theory. III. Quantization of Maxwell Equations and Weak Local Commutativity

Abstract: The problem of the quantization of the Maxwell equations is analyzed in connection with the basic assumptions of quantum field theory. It is shown that it is impossible to quantize the Maxwell equations by means of a potential ${A}_{\ensuremath{\mu}}(x)$ which is a weakly local field. Thus, a result which was known for the Coulomb gauge is shown to hold in general: The quantization of the Maxwell equations requires the use of a potential ${A}_{\ensuremath{\mu}}(x)$ which is both noncovariant and nonlocal. It is shown that a weakly local and/or covariant operator ${A}_{\ensuremath{\mu}}(x)$ can be introduced only in a Hilbert space in which the vectors corresponding to physical states do not form a dense set, and therefore unphysical states must be present. The connections with the Gupta-Bleuler formulation are discussed.

Quantum Phase Fluctuations in Resistive Circuits Containing Weakly Superconducting Junctions

Abstract: Experimental evidence is presented which shows that quantization of the phase integral is not a necessary condition for the occurrence of quantum interference effects in superconducting weak‐link circuits. Interference patterns observed with weak‐link geometries containing resistive sections differ from their superconducting couterparts only in the effect of Johnson noise which causes a random walk in quantum phase.

NMR Multiple Quantum Transitions by Second Quantization Formalism

Abstract: Single and multiple quantum transitions in NMR are calculated using a second quantization formalism. This leads to a great formal simplification with respect to the usual rotating frame treatment. The results strictly agree with the experimental data available for thiophene.

Relativistic quantum mechanics of fermions

Abstract: We present a modification of the Dirac equation that allows us to formulate a relativistic quantum mechanics for spin-1/2 fermions in an external electromagnetic field, with a probabilistic interpretation similar to that in nonrelativistic quantum mechanics and based on an indefinite charge density. We find that stationary states cannot be interpreted in this manner, and we replace them by quasistationary states. We also include a general discussion of the difficulties and possible generalizations of this approach.

Scattering formalism for non-localizable fields

Abstract: We consider the theory of a non-localizable relativistic quantum field Nonlocalizability means that the field is not a tempered distribution, but increases strongly for large momenta Local commutativity can then not be satisfied Instead we assume the existence of Green's functions with the usual analyticity properties We show that in such a theory theS-matrix can be defined, and its elements can be expressed in terms of the fields by the usual reduction formulae

The Quantization Program for General Relativity

Abstract: The problem of the construction of a quantum theory of gravitation is attacked by a variety of methods. The fundamental epistemological difficulties are ellucidated and certain novel qualitative features of the sought-for quantum theory are described.

Symmetric dirac bracket in classical mechanics.

Abstract: It is known that, in classical systems that have second‐class constraints which relate the canonical coordinates and momentum, the ordinary skew‐symmetric Poisson bracket must be replaced by the skew‐symmetric Dirac bracket. It is also known that in the process of quantization of such systems, the Dirac bracket replaces the Poisson bracket in its correspondence with the quantum commutators. In this paper we obtain the symmetric partner of the Dirac bracket, which is of interest not only to classical mechanics but also in regard to the quantization procedure; i.e., the quantization rules for systems which are restricted by second‐class constraints such that the commutation rules involve anticommutators (instead of commutators, as in certain fields with Fermi‐Dirac statistics) can be given in terms of this new symmetric bracket. This symmetric bracket is related to the Poisson‐Droz‐Vincent symmetric bracket.

Indefinite metric in massless quantum field theories of arbitrary spin

Abstract: The Gupta-Bleuler quantization procedure of electrodynamics is generalized to massless quantum field theories of higher spin without interaction, in particular to include the linearized form of a quantized gravitational theory. It is shown that a manifest Lorentz-invariant local formulation of a theory for spin-j massless particles requires in general the introduction of 2(j2+1) field components which transform under a reducible representation of the homogeneous Lorentz group and are linear operators in a state space with an indefinite metric. Using the spinor representation rather than the usual tensor representation the operators in momentum space can be easily subdivided into the two physical operators connected with the annihilation and creation of the two physical mass-zero modes and 2j2 ghost operators which can be arranged intoj2 pairs. Each operator pair is connected with annihilation and creation of two nonorthogonal norm-zero states, a «good» and a «bad» ghost. A physical interpretation of the theory is achieved by projection on a physical state space with positive semi-definite metric which consists in the invariant elimination of allj2 bad ghosts byj2 Gupta-type conditions. The physical unobservable admixture of thej2 good ghosts reflects the gauge degrees of freedom of equal dimension.

On Scattering and Bound States for a Singular Potential

Abstract: To understand the origin of the difficulties in the determination of the physical wavefunc­ tion for an attractive inverse square potential, we study a model in which the singularity at the origin is substituted by a repulsive core. The structure of the spectrum of energy levels is discussed in some detail. The physical interpretation of the solutions of the Schrodinger equation for a potential of the form - (-h 2 /2m) 11/ r 2 presents difficulties, which occur for 11 larger than (l + 1/2)\ where l is the angular momentum. The difficulties are due to the fact that the condition of square integrability usually imposed on the wavefunction is not sufficient in this case to determine phase shifts or energies of bound states. For strongly attractive singular potentials, as in the case of the attractive inverse square potential, both solutions of the wave equation are square integrable, so that Von Neumann's criterium fails to determine a unique solution. A solution can be built which is finite for r~oo, but it will be finite for every value of the energy from zero to minus infinity, so that no discrete energy spectrum can be determined. The problem of the determination of the energies of the bound states for the inverse square potential has been discussed by several authors. Some of these authors postulate additional conditions on the wavefunctions representing physical states so as to obtain a discrete energy spectrum. Shortley 1 ) discussed the quantum mechanical problem as related to the classical case, and did not try to eliminate the absence of quantization of the energy levels. Landau and Lif­ shitz2) showed how the lack of quantization is related to the singularity of the potential at the origin. Recently Guggenheim, 3 ) based on simple arguments of dimensional analysis, showed how it is impossible to define uniquely energy levels for the attractive inverse square potential if no extra parameter is pro­ vided. Case, 4 ) besides assuming the square integrability of the wavefunctions, introduced the extra condition that the wavefunctions representing physical states form an orthogonal set. This assumption is sufficient to define the spacing of