Untitled

Yi, Kyu Yang; Zheng, Yuan F.

doi:10.1023/a:1008800311277

Cited by 21 publications

(39 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Had one instead started with the Yang-Mills matrix quantum mechanics from the onset, then one would have obtained a linear Schrödinger equation with interactions taken care of by the Yang-Mills potential. This is what had been studied in the literature so far [3], with no definite, general conclusions about the bound state problem for strings and D-particles (see [4] for recent developments). In the present approach, we effectively reduce the quantum mechanics to a single body problem (the dynamics of the "fat brane" [34]), at the cost of obtaining a non-linear wave equation.…”

Section: B Stationary Solutionsmentioning

confidence: 84%

Nonlinear Schrödinger Dynamics of Matrix D-Branes

Mavromatos

Szabo²

2001

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

We formulate an effective Schrödinger wave equation describing the quantum dynamics of a system of D0-branes by applying the Wilson renormalization group equation to the worldsheet partition function of a deformed σ-model describing the system, which includes the quantum recoil due to the exchange of string states between the individual D-particles. We arrive at an effective Fokker-Planck equation for the probability density with diffusion coefficient determined by the total kinetic energy of the recoiling system. We use Galilean invariance of the system to show that there are three possible solutions of the associated non-linear Schrödinger equation depending on the strength of the open string interactions among the D-particles. When the open string energies are small compared to the total kinetic energy of the system, the solutions are governed by freely-propagating solitary waves. When the string coupling constant reaches a dynamically determined critical value, the system is described by minimal uncertainty wavepackets which describe the smearing of the D-particle coordinates due to the distortion of the surrounding spacetime from the string interactions. For strong string interactions, bound state solutions exist with effective mass determined by an energy-dependent shift of the static BPS mass of the D0-branes.Despite the enormous amount of activity over the past few years towards understanding the dynamics of Dirichlet p-branes [1], the problem of demonstrating that a system of N moving D-particles can form a bound state is still unresolved. It is relevant to the Matrix Theory conjecture [2] in which these particles are interpreted as Kaluza-Klein modes of 11dimensional M-Theory compactified on a circle and are described by the supersymmetric N × N matrix quantum mechanics that is obtained from dimensional reduction of N = 1 supersymmetric Yang-Mills theory in ten dimensions. The existence of such a tower of states is equivalent to the statement that the quantum mechanics admits exactly one bound state for each N. The original threshold bound state problem was addressed in [3] and recent progress has been made in [4]. However, beyond the proof of existence in the case N = 2, the general case N > 2 remains in large part an open problem. In this paper we shall address the bound state problem for a system of N non-relativistic, recoiling D0-branes by studying their moduli space dynamics in certain limits.The effective worldvolume dynamics of a single Dp-brane coupled to a worldvolume gauge field and to background supergravity fields is described by the action [1]

show abstract

Section: B Stationary Solutionsmentioning

confidence: 84%

Nonlinear Schrödinger Dynamics of Matrix D-Branes

Mavromatos

Szabo²

2001

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

show abstract

“…We will describe here how the results (1.16) are obtained and explain the reasons of disagreement between the results of the old [2] and new [11] calculations.…”

Section: Discussionmentioning

confidence: 99%

Normalized vacuum states in supersymmetric Yang–Mills quantum mechanics with any gauge group

Kač

Smilga

2000

Nuclear Physics B

View full text Add to dashboard Cite

We study the question of existence and the number of normalized vacuum states in N = 4 super-Yang-Mills quantum mechanics for any gauge group. The mass deformation method is the simplest and clearest one. It allowed us to calculate the number of normalized vacuum states for all gauge groups. For all unitary groups, # vac = 1, but for the symplectic groups [starting from Sp (6) ], for the orthogonal groups [starting from SO (8)] and for all the exceptional groups, it is greater than one. We also discuss at length the functional integral method. We calculate the "deficit term" for some non-unitary groups and predict the value of the integral giving the "principal contribution". The issues like the Born-Oppenheimer procedure to derive the effective theory and the manifestation of the localized vacua in the asymptotic effective wave functions are also discussed.

show abstract

“…The quantum equations of motion and the BRST transformations then again take the form (15), (18). In the co-ordinate representation, the BRSTinvariant inner product of two wave functions in the full ghost-extended Hilbert space now takes the form…”

Section: Lorenz Gaugementioning

confidence: 99%

A note on BRST quantization of SU(2) Yang-Mills mechanics

Fuster¹,

Holten²

2005

Journal of Mathematical Physics

View full text Add to dashboard Cite

The quantization of SU (2) Yang-Mills theory reduced to 0 + 1 space-time dimensions is performed in the BRST framework. We show that in the unitary gauge A 0 = 0 the BRST procedure has difficulties which can be solved by introduction of additional singlet ghost variables. In the Lorenz gaugeȦ 0 = 0 one has additional unphysical degrees of freedom, but the BRST quantization is free of the problems in the unitary gauge. *

show abstract

Untitled

Cited by 21 publications

References 17 publications

Nonlinear Schrödinger Dynamics of Matrix D-Branes

Nonlinear Schrödinger Dynamics of Matrix D-Branes

Normalized vacuum states in supersymmetric Yang–Mills quantum mechanics with any gauge group

A note on BRST quantization of SU(2) Yang-Mills mechanics

Contact Info

Product

Resources

About