7,009 research outputs found

### Stochastic Quantization of Axial Vector Gauge Theories

The stochastic quantization scheme proposed by Parisi and Wu in 1981 is known
to have differences from conventional quantum field theory in higher orders. It
has been suggested that some of these new features might give rise to a
mechanism to explain tiny fermion masses as arising due to radiative
corrections. In view of importance for need of going beyond the standard model,
in this article some features of U(1) axial vector gauge theory in Parisi Wu
stochastic quantization scheme are reported. Renormalizability of a massive
axial vector gague theory coupled to a massless fermion appears as one of the
important conclusions.Comment: 8page

### Quantum Mechanics in Pseudotime

Based on some results on reparmetrisation of time in Hamiltonian path
integral formalism, a pseudo time formulation of operator formalism of quantum
mechanics is presented. Relation of reparametrisation of time in quantum with
super symmetric quantum mechanics is established. We show how some important
concepts such as shape invariance and tools like isospectral deformation appear
in pseudo time quantum mechanics.Comment: 20 pages,22 Reference

### HAMILTONIAN PATH INTEGRAL QUANTIZATION IN ARBITRARY CO-ORDINATES AND EXACT PATH INTEGRATION

We briefly review a hamiltonian path integral formalism developed earlier by
one of us. An important feature of this formalism is that the path integral
quantization in arbitrary co-ordinates is set up making use of only classical
hamiltonian without addition of adhoc $\hbar^2$ terms. In this paper we use
this hamiltonian formalism and show how exact path integration may be done for
several potentials.Comment: LATEX, 35 Pages , compile twice to get equation numbers correct, No
Figures

### Local Scaling of Time in Hamiltonian Path Integration

Inspired by the usefulness of local scaling of time in the path integral
formalism, we introduce a new kind of hamiltonian path integral in this paper.
A special case of this new type of path integral has been earlier found useful
in formulating a scheme of hamiltonian path integral quantization in arbitrary
coordinates. This scheme has the unique feature that quantization in arbitrary
co-ordinates requires hamiltonian path integral to be set up in terms of the
classical hamiltonian only, without addition of any adhoc $O(\hbar ^2)$terms.
In this paper we further study the properties of hamiltonian path integrals in
arbitrary co-ordinates with and without local scaling of time and obtain the
Schrodinger equation implied by the hamiltonian path integrals. As a simple
illustrative example of quantization in arbitrary coordinates and of exact path
integration we apply the results obtained to the case of Coulomb problem in two
dimensions.Comment: LATEX, Compile twice to get equation numbers correct, 27 Pages, No
Figures

### Hamiltonian path integral quantization in polar coordinates

Using a scheme proposed earlier we set up Hamiltonian path integral
quantization for a particle in two dimensions in plane polar coordinates.This
scheme uses the classical Hamiltonian, without any $O(\hbar^2)$ terms, in the
polar varivables. We show that the propagator satisfies the correct
Schr\"{o}dinger equation.Comment: 15 pages, latex, no figure

### Newton's Equation on the kappa space-time and the Kepler problem

We study the modification of Newton's second law, upto first order in the
deformation parameter $a$, in the $\kappa$-space-time. We derive the deformed
Hamiltonian, expressed in terms of the commutative phase space variables,
describing the particle moving in a central potential in the
$\kappa$-space-time. Using this, we find the modified equations of motion and
show that there is an additional force along the radial direction. Using
Pioneer anomaly data, we set a bond as well as fix the sign of $a$. We also
analyse the violation of equivalence principle predicted by the modified
Newton's equation, valid up to first order in $a$ and use this also to set an
upper bound on $a$.Comment: 8 pages, Minor changes in subsection III A made for clarity, to
appear in Mod. Phys. Lett.

### Coefficient Estimates for Inverses of Starlike Functions of Positive Order

In the present paper, the coefficient estimates are found for the class
$\mathcal S^{*-1}(\alpha)$ consisting of inverses of functions in the class of
univalent starlike functions of order $\alpha$ in $\mathcal D=\{z\in\mathbb
C:|z|<1\}$. These estimates extend the work of {\it Krzyz, Libera and
Zlotkiewicz [Ann. Univ. Marie Curie-Sklodowska, 33(1979), 103-109]} who found
sharp estimates on only first two coefficients for the functions in the class
$\mathcal S^{*-1}(\alpha)$. The coefficient estimates are also found for the
class $\sum^{*-1}(\alpha)$, consisting of inverses of functions in the class
$\sum^*(\alpha)$ of univalent starlike functions of order $\alpha$ in $\mathcal
V=\{z\in\mathbb C:1<|z|<\infty\}$. The open problem of finding sharp
coefficient estimates for functions in the class $\sum^*(\alpha)$ stands
completely settled in the present work by our method developed here.Comment: 12 page

### Construction of 2nd stage shape invariant potentials

We introduce concept of next generation shape invariance and show that the
process of shape invariant extension can be continued indefinitely.Comment: 5 page

### Uniformly accelerating observer in $\kappa$-deformed space-time

In this paper, we study the effect of $\kappa$-deformation of the space-time
on the response function of a uniformly accelerating detector coupled to a
scalar field. Starting with $\kappa$-deformed Klein-Gordon theory, which is
invariant under a $\kappa$-Poincar\'e algebra and written in commutative
space-time, we derive $\kappa$-deformed Wightman functions, valid up to second
order in the deformation parameter $a$. Using this, we show that the first
non-vanishing correction to the Unruh thermal distribution is only in the
second order in $a$. We also discuss various other possible sources of
$a$-dependent corrections to this thermal distribution.Comment: 12 pages, minor changes, to appear in Phys. Rev.

### Non-Commutative space-time and Hausdorff dimension

We study the Hausdorff dimension of the path of a quantum particle in
non-commutative space-time. We show that the Hausdorff dimension depends on the
deformation parameter $a$ and the resolution $\Delta x$ for both
non-relativistic and relativistic quantum particle. For the non-relativistic
case, it is seen that Hausdorff dimension is always less than two in the
non-commutative space-time. For relativistic quantum particle, we find the
Hausdorff dimension increases with the non-commutative parameter, in contrast
to the commutative space-time. We show that non-commutative correction to Dirac
equation brings in the spinorial nature of the relativistic wave function into
play, unlike in the commutative space-time. By imposing self-similarity
condition on the path of non-relativistic and relativistic quantum particle in
non-commutative space-time, we derive the corresponding generalised uncertainty
relation.Comment: 16 pages, 3 figures, minor changes, to appear in IJMP

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