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A gauge field theory is considered which admits p-dimensional topological defects, expanding the equations of motion in powers of the defect thickness. In this way an effective action and effective equation of motion is derived for the defect in terms of the coordinates of the p-dimensional worldsurface defined by the history of the core of the defect.
A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.
Response of magnetron and vacuum gauges aboard explorer xvii measuring temperature, pressure, and density of upper atmosphere
The polymer expansion is a formal algebraic identity between a partition function and logarithm in statistical physics problems. The expansion gives a systematic method to control the free energy or to establish exponential tree-graph decay of connected correlations. Here, the convergence properties of the polymer expansion are analyzed in connection with three practical examples, including: intersecting bonds in chemical polymer chains; a connected closed hypersurface built from the (d-1)-faces of the d-dimensional unit cubes; and the set of Feynamn diagrams in the perturbation series of the Euclidean field theory partition function Z. The example of connected polymer chains is generalized to apply to other lattice models, including n-state Ising models at high temperature; short range lattice gases at high temperature; and weak coupling lattice field and gauge theories.
A scale-covariant theory of gravitation is presented which is characterized by a set of equations that are complete only after a choice of the scale function is made. Special attention is given to gauge conditions and units which allow gravitational phenomena to be described in atomic units. The generalized gravitational-field equations are derived by performing a direct scale transformation, by extending Riemannian geometry to Weyl geometry through the introduction of the notion of cotensors, and from a variation principle. Modified conservation laws are provided, a set of dynamical equations is obtained, and astrophysical consequences are considered. The theory is applied to examine certain homogeneous cosmological solutions, perihelion shifts, light deflections, secular variations of planetary orbital elements, stellar structure equations for a star in quasi-static equilibrium, and the past thermal history of earth. The possible relation of the scale-covariant theory to gauge field theories and their predictions of cosmological constants is discussed.
Many cosmological models rely on large couplings of axions to gauge fields. Examples include theories of magnetogenesis, inflation on a steep potential, chiral gravitational waves, and chromonatural inflation. Such theories require a mismatch between the axion field range and the mass scale appearing in the aFF~ coupling. This mismatch suggests an underlying monodromy, with the axion winding around its fundamental period a large number of times. We investigate the extent to which this integer can be explained as a product of smaller integers in a UV completion: in the parlance of our times, can the theory be “clockworked”? We argue that a clockwork construction producing a potential μ4cos(ajFa) for an axion of fundamental period Fa will obey the constraint μ < Fa. For a some applications, including chromonatural inflation with sub-Planckian field range, this constraint obstructs a clockwork UV completion. Alternative routes to a large coupling include fields of large charge (an approach limited by strong coupling) or kinetic mixing (requiring a lighter axion). Our results suggest that completions of axion cosmologies that explain the large parameter in the theory potentially alter the phenomenological predictions of the model.
The method described in the present report makes it possible to obtain interferometer records with the aid of any one of the available Schlieren optics by the addition of very simple expedients, which fundamentally need not to be inferior to those obtained by other methods, such as the Mach-Zehnder interferometer, for example. The method is based on the fundamental concept of the phase-contrast process developed by Zernike, but which in principle has been enlarged to such an extent that it practically represents an independent interference method for general applications. Moreover, the method offers the possibility, in case of necessity, of superposing any apparent wedge field on the density field to be gauged. The theory is explained on a purely physical basis and illustrated and proved by experimental data. A number of typical cases are cited and some quantitative results reported.
Assuming that the divergence of the energy-momentum tensor is nonzero leads to a class of theories with consistent field equations and gauge conditions as well as compatibility with the Newtonian limit of the conservation laws. Both the Einstein and the Brans-Dicke theories are used as models, but the extension to other viable theories such as vector-metric and two-metric theories is possible. One particularly interesting theory emerges that agrees with the ordinary Brans-Dicke theory except for the post-Newtonian parameter zeta sub 2, which predicts nonconservation of total momentum. Unfortunately, no accurate experimental limits for this parameter are known. It thus remains for future experiments in lunar-laser ranging to test this theory.
Classical non-topological soliton configurations are considered within the theory of a complex scalar field with a gauged U symmetry. Their existence and stability against dispersion are demonstrated and some of their properties are investigated analytically and numerically. The soliton configuration is such that inside the soliton the local U symmetry is broken, the gauge field becomes massive and for a range of values of the coupling constants the soliton becomes a superconductor pushing the charge to the surface. Furthermore, because of the repulsive Coulomb force, there is a maximum size for these objects, making impossible the existence of Q-matter in bulk form. Also briefly discussed are solitons with fermions in a U gauge theory.
The fundamental equations of magnetospheric plasma electrodynamics are considered from a theoretical standpoint that stresses the basic equivalence of various seemingly different formal representations. The mathematical properties of vector fields are reviewed, and their implications in electrodynamics are studied. The irrotational and solenoidal parts of the electric field are associated with two physically distinct types of sources. Relativistic covariance and gauge invariance in electromagnetic theory are reviewed and discussed in the context of an approach in which the mathematical properties of vector fields are taken as primary concepts. Special attention is given to the use and interpretation of the Coulomb gauge potential functions. This choice of gauge is sometimes regarded with undue suspicion, possibly because of a certain paradox concerning causality. The paradox is discussed and resolved. Useful properties of the Coulomb gauge are identified. These need not be limited to the case of slow time variations and can extend beyond the limits of validity of ideal MHD theory.
This survey paper describes recent developments in the area of parametrized variational principles (PVP's) and selected applications to finite-element computational mechanics. A PVP is a variational principle containing free parameters that have no effect on the Euler-Lagrange equations. The theory of single-field PVP's based on gauge functions (also known as null Lagrangians) is a subset of the inverse problem of variational calculus that has limited value. On the other hand, multifield PVP's are more interesting from theoretical and practical standpoints. Following a tutorial introduction, the paper describes the recent construction of multifield PVP's in several areas of elasticity and electromagnetics. It then discusses three applications to finite-element computational mechanics: the derivation of high-performance finite elements, the development of element-level error indicators, and the constructions of finite element templates. The paper concludes with an overview of open research areas.
The possible consequences of forming cosmic strings and superconducting cosmic strings in the early universe are discussed. Lecture 1 describes the group theoretic reasons for and the field theoretic reasons why cosmic strings can form in spontaneously broken gauge theories. Lecture 2 discusses the accretion of matter onto string loops, emphasizing the scenario with a cold dark matter dominated universe. In lecture 3 superconducting cosmic strings are discussed, as is a mechanism which leads to the formation of structure from such strings.
A study discussing and investigating the role of inductive electric fields in substorm development is presented. It is common to use the scalar potential phi to calculate the electrostatic field E(sup ES)-(inverted Delta)(phi). However, vector potential A has not been extensively used to analyze results by the relation for the inductive electric field E(sup IND)-delta A/delta t. Because of the weak dependence in distance (1/r) these potentials show the effect of distant sources, unlike MHD (Magnetohydrodynamic) theory which is strictly local. The two can be separated by the choice of the Coulomb (transverse) gauge. It is proper to consider that the plasma polarizes to counteract the activation of the inductive electric field; this is a matter of cause and effect. However, such polarization produces a curl free electrostatic field and thus cannot alter the electromotive force due to induction. This idea has some interesting consequences for plasma physics, including violations of MHD theory, creation of the substorm current diversion, and a fresh look at dayside merging via plasma transfer events.
We study magnetically charged classical solutions of a spontaneously broken gauge theory interacting with gravity. We show that nonsingular monopole solutions exist only if the Higgs field vacuum expectation value v is less than or equal to a critical value v sub cr, which is of the order of the Planck mass. In the limiting case, the monopole becomes a black hole, with the region outside the horizon described by the critical Reissner-Nordstrom solution. For v less than v sub cr, we find additional solutions which are singular at f = 0, but which have this singularity hidden within a horizon. These have nontrivial matter fields outside the horizon, and may be interpreted as small black holes lying within a magnetic monopole. The nature of these solutions as a function of v and of the total mass M and their relation to the Reissner-Nordstrom solutions is discussed.
The Smit-Swift-Aoki formulation of a lattice chiral gauge theory is presented. In this formulation the Wilson and other non invariant terms in the action are made gauge invariant by the coupling with a nonlinear auxilary scalar field, omega. It is shown that omega decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, explicit ghost fields are necessary to ensure decoupling. These theories can give rise to the correct continuum limit. Similar considerations apply to schemes with mirror fermions. Simpler cases with a global chiral symmetry are discussed and it is shown that the theory becomes free at decoupling. Recent numerical simulations agree with those considerations.
Attempt to develop a gauge-invariant theory of the motion of singularities in an n-dimensional Riemannian space. A gauge-invariant theory is developed for a nongeodetic particle represented by a time-like world line in the linearized field theory. The solution of the basic algebraic and differential equations is to be constructed from the source line, the future null cones emanating from it, a scale factor, and nothing else, and the leading term of the solution is the Schwarzschild field. A class of possible solutions is examined, and it is shown that this class contains just one acceptable member - namely, a particle in constant acceleration.
The gauge theory of gravitation introduced by Mansouri and Chang (1976) is investigated; a symbolic manipulation computer system generates the Mansouri-Chang field equations in various coordinate systems. It is found that all vacuum Einstein spaces are vacuum Mansouri-Chang spaces in four dimensions, though for higher dimensions an Einstein vacuum space is not generally a Mansouri-Chang solution. The possibility that no solutions of the Mansouri-Chang equations are not Einstein vacuum spaces is discussed.
An effective theory of superconductivity based on a microscopic theory of the T- and P-breaking spin-liquid state is proposed. There are two independent gauge invariances broken by two separate condensates. The theory may be useful for phenomenological calculations. In particular, it is found that the H(c1) are different for magnetic fields with opposite orientations. It is also found that the polarization of an electromagnetic wave is rotated after reflection from these T- and P-breaking superconductors.