Lagrangian versus Quantization
We discuss examples of systems which can be quantized consistently, although they do not admit a Lagrangian description.
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arXiv subjects
Ciprian Acatrinei
Publications and source records attributed to Ciprian Acatrinei.
A note on the decay of noncommutative solitons
We propose an ansatz for the equations of motion of the noncommutative model of a tachyonic scalar field interacting with a gauge field, which allows one to find time-dependent solutions describing decaying solitons. These correspond to the collapse of lower dimensional branes obtained through tachyon condensation of unstable brane systems in string theory.
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Noncommutative radial waves
We study radial waves in (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At radius much larger than the noncommutativity scale $\sqrtθ$, one recovers the usual commutative behaviour. At small distances, classical divergences are smoothed out by noncommutativity.
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Bilocal Dynamics in Quantum Field Theory
An essential aspect of noncommutative field theories is their bilocal nature. This feature, and its role in the IR/UV mixing, are discussed using a canonical quantization procedure developed recently.
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Canonical Quantization of Noncommutative Field Theory
A simple method to canonically quantize noncommutative field theories is proposed. As a result, the elementary excitations of a (2n+1)-dimensional scalar field theory are shown to be bilocal objects living in an (n+1)-dimensional space-time. Feynman rules for their scattering are derived canonically. They agree, upon suitable redefinitions, with the rules obtained via star-product methods. The IR/UV connection is interpreted within this framework.
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Path Integral Formulation of Noncommutative Quantum Mechanics
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic oscillator is calculated.
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Comments on Noncommutative Particle Dynamics
We discuss a version of Hamiltonian (2+1)-dimensional dynamics, in which one allows nonvanishing Poisson brackets also between the coordinates, and between the momenta. The resulting equations of motion are not any more derivable from a Lagrangian. However, taking a specific limit, in which the symplectic form becomes singular, one can recover a first-order Lagrangian description. This signals the dimensional reduction of the phase-space to half its initial number of degrees of freedom. We reach the same limit from another point of view, studying a particular form of the Poisson brackets, which is singled out geometrically and easy to handle algebraically. For comparison, a discussion of quantum mechanics with extended Heisenberg algebra is included. The quantum theory constrains the antisymmetric matrix providing the algebra to the above mentioned classically singular limit.
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Effects of Magnetic Fields on String Pair Creation
The rate of pair production of open strings in general uniform electromagnetic fields is calculated in various space-time dimensions. The corrections with respect to the case of pure electric backgrounds are displayed. In particular, a contribution in the form of a Born-Infeld action is derived and its role in the present context emphasized
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D-particles in the space-time of the shock wave
We study the interaction of two D-particles in the space-time of the shock wave. We first write the amplitude in string theory and find that, at large distances from the shock-wave source, the O(v^4) term in the relative velocity v is an α'-independent function of the interbrane separation b. The amplitude is therefore that of supergravity--for large b, only closed-string massless modes contribute. We then show how the same result is obtained in the matrix model (at small b) by setting up the formulation of the dimensionally reduced super Yang-Mills theory in the curved background of the shock wave.
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