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The applications of Josephson junctions to the measurement of low-frequency magnetic fields and voltages are reviewed. The relevant ideas of flux quantization and Josephson tunneling are very briefly reviewed, and the various methods of making Josephson junctions mentioned. The two basic types of magnetic sensor, the dc superconducting quantum interference device (SQUID) and the RF SQUID, are described in some detail. Their theory of operation, noise limitations, and application to practical devices are discussed. The resolution of SQUID's commonly used in an analog mode is 10-4to 10-3Φ 0 /√Hz, where Φ 0 is the flux quantum. The basic sensor may be used in conjunction with a flux transformer to measure magnetic fields (with a resolution of 10-14T/√Hz), magnetic-field gradients (with a resolution of 10-12T/m/√Hz), and magnetic susceptibilities. The SQUID may also be used as a voltmeter. The resolution is limited by the Johnson noise developed in the resistance of the low-temperature circuit, provided that this resistance is not too large: the upper limit in the liquid-He4temperature range appears to be a few tens of ohms.

In 1924 Bose,1 undertaking to deal statistically with "light quanta," hit upon a method of using generalized co6rdinates which enabled him to derive the Planck law of black-body radiation without making use, as others had done, of conceptions taken from the classical mechanics. Einstein,2 adopting the Bose statistical method, applied it to the discussion of quantization of energy in an ideal monatomic gas, and the consequent degeneration [Entartung] of the gas-that is, the degree of its departure from the classical gas-laws. He reached the following conclusion: "The mean energy of the gas molecules (as well as the pressure) at the temperature is therefore always less than the classical value." In 1926 Fermi3 attacked the same problem that Einstein had discussed. He used the same general statistical method that Bose had invented but introduced in its application a certain limiting assumption, with the following explanation: "Now a short time ago the rule was proposed by Pauli4 . . . that when in an atom an electron exists the quantum numbers of which (the magnetic quantum number included) have definite values, there can be in the atom no other electron whose path is characterized by the same numbers. In other words, a quantum orbit (in an external magnetic field) is already completely occupied by a single electron." "Since this rule of Pauli has proved extremely fruitful in the explanation of spectroscopic facts, we propose to inquire whether it is not also of some use for the problem of the quantization of ideal gases." "We shall therefore in what follows assume that at most one molecule with given quantum numbers can exist in our gas; as quantum numbers not only those here come into consideration which belong to the internal motions of the molecule but also those which determine its motion of translation."

Application of half quantum numbers to the theory of the rotational specific heat of hydrogen.—It is shown from a consideration of infra-red rotation-oscillation spectra, that the lowest possible azimuthal quantum number for a non-oscillating rotating molecule of the rigid "dumb-bell" model can have only the values zero, one, or one-half. An elementary theory of quantization in space for the new case of half quantum numbers is then developed which shows that the a priori probabilities for successive levels of rotational energy stand in the ratios of 1, 2, 3,.... The specific heat curve for diatomic hydrogen to 300°K is then calculated on the basis of the energy levels and of a priori probabilities corresponding to half quantum numbers, and is compared with the experimental points and with the curves calculated by Reiche using zero and one as the lowest possible azimuthal quantum number. At low temperatures the new curve agrees with the experimental data as well as any curve of Reiche's. At the higher temperatures, none of the curves agree with all the experimental points. The moment of inertia for the hydrogen molecule corresponding to the new curve is J=1.387×10^-41 gm cm2, about two-thirds the values assumed by Reiche, 2.095 to 2.293×10^-41, and agrees better with the conclusion of Sommerfeld from the separation of lines in the many lined spectrum of hydrogen, that the moment of inertia of an excited hydrogen molecule is 1.9×10^-41 gm cm2, which should be greater than that of the unexcited molecules involved in specific heats. Hence the possibility of half quantum numbers seems worthy of consideration.

It has been pointed out by Wigner that the consistency requirement between the Lagrange and Heisenberg equations of motion does not uniquely determine the canonical commutation relations, at least for one‐dimensional systems. It is shown here that this ambiguity does not arise in local field theory whose basic equal‐time commutators commute with the translation operator.

The goal of quantum field theory is a description of elementary particles. When successful, this description should be both a mathematical theory and a law of nature. In our approach, we emphasize the construction of specific field theory models. The first motive for this emphasis is the mathematical consistency of quantum field theory. In addition, we follow closely the formal ideas of physics in order to provide a more solid foundation for the main task of quantum field theory: the study of elementary particles. It is clear by now that the first motive has been attained in two spacetime dimensions. In two space-time dimensions, quantum fields with nonlinear interactions have been constructed [1], [2]. For the polynomial boson (^(0)2) interactions with small coupling constant, all the Wightman axioms have been verified [5]. We announce two new results. The first is an estimate which is a major technical step toward establishing the above results in three space-time dimensions. The second result concerns the physical interpretation of our two dimensional models (the second motive of our study). In ( )2 models with a small coupling constant, we establish the existence of particles and we verify the Haag-Ruelle axioms for scattering. Thus we conclude that the ^((/>)2 model has the qualitative structure required for the description of (many particle) scattering experiments. In our first result we consider the $3 interaction: a $ 4 coupling in the interaction Hamiltonian for boson fields in three space-time dimensions. We introduce a space cut-off g e CQ(R), 0 ^ 0 ^ 1, in the interaction Hamiltonian density, and we let the resulting total Hamiltonian (with infinite counterterms from second and third order perturbation theory) be denoted H(g). Let A(g) denote the set of points within distance 1 of supp g.

Made available in DSpace on 2022-04-29T08:43:47Z (GMT). No. of bitstreams: 0 Previous issue date: 1969-02-01 Instituto de Física Teorica, São Paulo

There is no dearth of experimental evidence to indicate that real space-time is a four-dimensional manifold. At present there is much less certainty in attributing dimensions to the charge space of heavy particles, and it may be worth while to review various hypotheses and the meager experimental evidence in this regard. The Clebsch-Gordon coefficients for /-spin that appear in the =-N (nucleon) scattering resonance imply at least a two-dimensional space for unitary transformations (~), which are conveniently represented in the usual terms of rotations in a three-dimensional space. The apparent symmetry between E and N can be emphasized to the maximum extent by regarding the charge displacement number a = q I z of heavy particles as the third component of another vector A in charge space (~). If A is to be independent of / , there must be added an independent pair of coordinates for the unitary transformations

Results of a preceding paper on pure operations are generalized. The application to local field theory is discussed in some detail.

Following Weisskopf, the kinematics of quantum mechanics is shown to lead to a modified charge distribution for a test electron embedded in the Fermi-Dirac vacuum with interesting consequences.

While direct-interaction particle theories are generally thought to be incompatible with relativity in classical physics, such relativistic theories in quantum mechanics have recently attracted attention. The reasons for rejecting these theories in classical physics are based on the consideration of world lines, while relativistic quantum mechanics has no covariant position operator so that the classical refuting argument cannot be adapted.

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.

Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way. The probability that a particle will be found to have a path x(t) lying somewhere within a region of space time is the square of a sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of ℏ) for the path in question. The total contribution from all paths reaching x, t from the past is the wave function ψ(x, t). This is shown to satisfy Schroedinger's equation. The relation to matrix and operator algebra is discussed. Applications are indicated, in particular to eliminate the coordinates of the field oscillators from the equations of quantum electrodynamics.

The classical mechanics of indistinguishable particles discussed in I is further developed. The mechanical foundations of thermodynamics are discussed with the classical wave theory and the "quantized" fields in phase space. It is shown that the formalism eliminates automatically the Gibbs paradox. The classical statistics is treated with the Gibbs-von Neumann method and also by a generalized form of the Boltzmann method which allows to take into account the interactions. The introduction of finite cells in phase space leads to formulas similar to those of the quantal statistics for free particles, but no, more so for interacting particles. The statistical treatment of the «quantized» field in phase space leads immediately to the canonical grand ensemble. It is shown that the theory of the «quantized» fields in phase space can be derived from the theory of a «non-quantized» field in phase space, in which there are only continuous distributions of matter, by a procedure of «quantization» altogether similar to that of the quantum theory of fields, but not involving the Planck constant, or any other universal constant. The «non-quantized» field in phase space corresponds to a theory less accurate than the classical mechanics and gives an approximation of the same kind as the molecular chaos hypothesis of the kinetic gas theory, it contains both the dynamics and the heat theory of a continuous medium. A new derivation of the Boltzmann equation involving a special kind of time average is given and a similar equation is established for the two particle distribution function. © 1953 Società Italiana di Fisica., SCOPUS: ar.j, La pagination indiquée dans la zone "Pages" est celle du tiré à part, numérisé par les Bibliothèques de l'ULB. La pagination, telle qu'elle apparaît dans la revue est pp. 419-472, info:eu-repo/semantics/published

Two examples are presented: The first shows that a potentialV(x) can be in the limit circle case at ∞ even if the classical travel time to ∞ is infinite. The second shows thatV(x) can be in the limit point case at ∞ even though the classical travel time to infinity is finite. The first example illustrates the reflection of quantum waves at sharp steps. The second example illustrates the tunnel effect.

The quantum theory of diatomic dipoles.---Using the treatment of Pauli, an expression for the dielectric constant of a diatomic dipole gas is obtained, in which half-quantum numbers are used. It is shown that for cases of practical interest the approximation suggested by Pauli is not valid; hence numerical values of the temperature-function $C$ have been calculated and tabulated.Application to experimental measurements.---The theory has been applied in the interpretation of Zahn's measurements of the dielectric constants of the hydrogen halides. The electric moments of molecules of hydrogen chloride, bromide, and iodide were found to be 0.3316, 0.252, and 0.146\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}18}$ cgsu respectively; i.e., only about one-third of the values given on the basis of the classical theory. Moreover, the values 0.00077 and 0.00102 for $4\ensuremath{\pi}{N}_{0}\ensuremath{\alpha}$ for hydrogen chloride and bromide, in which $\ensuremath{\alpha}$ is the coefficient of induced polarization, are shown to be in better agreement with measurements of indices of refraction than are the classical theory values. A discussion is given of possible inaccuracies in the theory, of the choice of quantum numbers, and of the possibility of weak quantization.

Galilean quantum field theories, i.e. kinematically consistent non-relativistic quantum theories with an infinite number of degrees of freedom, are considered. These theories transcend the frame of ordinary quantum mechanics by allowing genuine particle production processes to be described. The general structure of such theories is discussed and contrasted with the typical structure of relativistic quantum field theories which they may serve to illustrate a contrario. Despite the mass superselection rule, and due to the weakening of local commutativity conditions, galilean quantum field theories are much less constrained than relativistic ones. The CPT and spin-and-statistics theorems do not hold here, neither does Haag's theorem.