Time-like Gauge Research Articles

Covariantized matrix theory for D-particles

We reformulate the Matrix theory of D-particles in a manifestly Lorentz-covariant fashion in the sense of 11 dimesnional flat Minkowski space-time, from the viewpoint of the so-called DLCQ interpretation of the light-front Matrix theory. The theory is characterized by various symmetry properties including higher gauge symmetries, which contain the usual SU($N$) symmetry as a special case and are extended from the structure naturally appearing in association with a discretized version of Nambu's 3-bracket. The theory is scale invariant, and the emergence of the 11 dimensional gravitational length, or M-theory scale, is interpreted as a consequence of a breaking of the scaling symmetry through a super-selection rule. In the light-front gauge with the DLCQ compactification of 11 dimensions, the theory reduces to the usual light-front formulation. In the time-like gauge with the ordinary M-theory spatial compactification, it reduces to a non-Abelian Born-Infeld-like theory, which in the limit of large $N$ becomes equivalent with the original BFSS theory.

Calculation of static interquark potential in a string model in a timelike gauge

The quantum theory of a relativistic string with fixed ends is constructed using a timelike gauge. A gauge condition is introduced into the reparametrization-invariant string action. In the theory, there are no restrictions on the space-time dimension and there are no tachyon states. The constraints and gauge conditions are satisfied in the quantum case only on the average, at the level of the matrix elements between the physical state vectors. The string generates a static potential V(R) = ..sqrt gamma../sup 2/R/sup 2/ + epsilon /sub 0/, where the constant epsilon/sub 0/ is a free parameter of the theory which can be determined from experiment.

Construction of physical states in Yang-Mills theory: The time-like gauge

We construct physical states in pure Yang-Mills theory in the time-like gauge A α 0 = 0. We also construct a complete basis in the physical subspace of Hilbert space. Comparison is made with a recent paper by Eylon.

Quantum Poincaré covariance of the two-dimensional string

We show that the free massive quantum string in two space-time dimensions is Poincar\'e covariant. This is true for both lightlike and timelike gauge choices. When the massless limit is taken, the massless string is also seen to be Poincar\'e covariant. The set of classical string variables which is chosen to define the quantum theory drastically affects the proof of Poincar\'e covariance and also the mass spectrum. We therefore suggest that other dynamical systems may exhibit similar phenomena.

Quantization of a massless spinning string in a timelike gauge

The quantization programme for a massless relativistic spinning string in a timelike orthonormal gauge has been worked out in the manner of Goddard, Hanson and Ponzano using Dirac’s approach by constructing classical analogues of DDF-type operators of the Neveu-Schwarz dual-resonance model. The programme has been shown to be completely equivalent to that in a lightlike orthonormal gauge. The canonical quantization is seen to be possible only in 10, space-time dimensions with the value of the Regge intercept of 1/2.

Study of the longitudinal kink modes of the string

We examine the massless limit of a model for the massive relativistic Nambu string. The system possesses longitudinal kink modes excluded from the standard lightlike gauge treatment. We demonstrate the equivalence of these modes to those proposed by Patrascioiu. The classical nonlinear field theory of the two-dimensional string is shown to be a completely integrable Hamiltonian system. The Hamiltonian is expressed in terms of normal-mode action variables alone; the mass-squared spectrum is linear in the Bohr-Sommerfeld approximation. The difficulties of canonical quantization are exposed using a particular timelike gauge which admits commuting center-of-mass coordinates.

The quantization of a massless relativistic string in a time-like gauge

The massless relativistic string is quantized in a time-like orthonormal gauge. The results are completely equivalent to those obtained in the light-like case. In particular, a strictly canonical quantization procedure succeeds only when the dimension of space-time is 26. The discussion is based on Dirac's formalism for contrained systems and the introduction of classical variables analogous to those defined by Del Giudice, Di Vecchia and Fubini in the dual model.