Transformation Laws Of Fields Research Articles

ON THE SYMMETRIC SPACE σ-MODEL KINEMATICS

The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.

Einstein?s Investigations of Galilean Covariant Electrodynamics Prior to 1905

Einstein learned from the magnet and conductor thought experiments how to use field transformation laws to extend the covariance to Maxwell’s electrodynamics. If he persisted in his use of this device, he would have found that the theory cleaves into two Galilean covariant parts, each with different field transformation laws. The tension between the two parts reflects a failure not mentioned by Einstein: that the relativity of motion manifested by observables in the magnet and conductor thought experiment does not extend to all observables in electrodynamics. An examination of Ritz’s work shows that Einstein’s early view could not have coincided with Ritz’s on an emission theory of light, but only with that of a conveniently reconstructed Ritz. One Ritz-like emission theory, attributed by Pauli to Ritz, proves to be a natural extension of the Galilean covariant part of Maxwell’s theory that happens also to accommodate the magnet and conductor thought experiment. Einstein's famous chasing a light beam thought experiment fails as an objection to an ether-based, electrodynamical theory of light. However it would allow Einstein to formulate his general objections to all emission theories of light in a very sharp form. Einstein found two well known experimental results of 18th and19th century optics compelling (Fizeau’s experiment, stellar aberration), while the accomplished Michelson-Morley experiment played no memorable role. I suggest they owe their importance to their providing a direct experimental grounding for Lorentz’ local time, the precursor of Einstein’s relativity of simultaneity, and do it essentially independently of electrodynamical theory. I attribute Einstein’s success to his determination to implement a principle of relativity in electrodynamics, but I urge that we not invest this stubbornness with any mystical prescience.

Free field dynamics in the generalized AdS (super)space

Pure gauge representation for general vacuum background fields (Cartan forms) in the generalized AdS superspace identified with OSp(L,M) is found. This allows us to formulate dynamics of free massless fields in the generalized AdS space–time and to find their (generalized) conformal and higher spin field transformation laws. Generic solution of the field equations is also constructed explicitly. The results are obtained with the aid of the star product realization of ortosymplectic superalgebras.

ON THE BRST APPROACH TO TWO-DIMENSIONAL GRAVITY IN THE LIGHT-CONE GAUGE

The BRST approach to two-dimensional gravity coupled to conformal field theories is discussed. The ordinary BRST symmetry acts only on the left-moving sector of the theory. It is found that there exists a BRST-like symmetry also in the right-moving sector. The conserved charge of this new symmetry is found to be nilpotent. This symmetry is a result of a redundancy of the parametrization of the gravitational field in terms of a scalar field. We propose that the physical states of the theory should belong to the cohomology of this BRST-like charge to eliminate the redundancy. It is also discussed how to derive the BRST charge from the action and the transformation laws of fields.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities.

Geometrical transformation laws of fields in superunified theories

We present a systematic model-independent method of obtaining off-the-mass-shell transformation laws of fields in superunified theories. The method is applied to pure gravity, gravity coupled to Yang-Mills, conformal gravity, OSp( N;4) supergravity, and conformal supergravity theories.

The conformal group, its casimir operators, and a four-position operator

We are investigating a class of representations of the conformal group which are physically interesting because there exists a position-time 4-vector operator within them and, related to this, because they are used in field transformation laws. We show that in these representations the three Casimir operators of the group have a very simple interpretation; we discuss when these representations are irreducible and we show that this 4-position operator can be expressed in terms of the generators of the group.

Finite-component field representations of the conformal group

We review work done on realization of broken symmetry under the conformal group of space-time in the framework of finite-component field theory. Topics discussed include: Most general transformation law of fields over Minkowski space. Consistent formulation of an orderly broken conformal symmetry in the framework of Lagrangian field theory; algebra of currents and their divergences; Manifestly conformally covariant fields and their couplings.