4,114 research outputs found
New Ansatz for Metric Operator Calculation in Pseudo-Hermitian Field Theory
In this work, a new ansatz is introduced to make the calculations of the
metric operator in Pseudo-Hermitian field theory simpler. The idea is to assume
that the metric operator is not only a functional of the field operators
and its conjugate field but also on the field gradient .
Rather than the locality of the metric operator obtained, the ansatz enables
one to calculate the metric operator just once for all dimensions of the
space-time. We calculated the metric operator of the scalar field
theory up to first order in the coupling. The higher orders can be conjectured
from their corresponding operators in the quantum mechanical case available in
the literature. We assert that, the calculations existing in literature for the
metric operator in field theory are cumbersome and are done case by case
concerning the dimension of space-time in which the theory is investigated.
Moreover, while the resulted metric operator in this work is local, the
existing calculations for the metric operator leads to a non-local one. Indeed,
we expect that the new results introduced in this work will greatly lead to the
progress of the studies in Pseudo-Hermitian field theories where there exist a
lack of such kind of studies in the literature. In fact, with the aid of this
work a rigorous study of a -symmetric Higgs mechanism can be
reached.Comment: In this version, for a more illustrative presentation, we used the
i\phi^3 theory to show that the new ansatz introduced is applicabl
Vacuum Stability of the -Symmetric Scalar Field Theory
In this work, we study the vacuum stability of the classical unstable scalar field potential. Regarding this, we obtained the
effective potential, up to second order in the coupling, for the theory in
and space-time dimensions. We found that the obtained effective
potential is bounded from below, which proves the vacuum stability of the
theory in space-time dimensions higher than the previously studied case.
In our calculations, we used the canonical quantization regime in which one
deals with operators rather than classical functions used in the path integral
formulation. Therefore, the non-Hermiticity of the effective field theory is
obvious. Moreover, the method we employ implements the canonical equal-time
commutation relations and the Heisenberg picture for the operators. Thus, the
metric operator is implemented in the calculations of the transition
amplitudes. Accordingly, the method avoids the very complicated calculations
needed in other methods for the metric operator. To test the accuracy of our
results, we obtained the exponential behavior of the vacuum condensate for
small coupling values, which has been obtained in the literature using other
methods. We assert that this work is interesting, as all the studies in the
literature advocate the stability of the theory at
the quantum mechanical level while our work extends the argument to the level
of field quantization.Comment: 20 pages, 4 figures, appendix added and more details have been added
to
Effective Field calculations of the Energy Spectrum of the -Symmetric () Potential
In this work, we show that the traditional effective field approach can be
applied to the -symmetric wrong sign () quartic
potential. The importance of this work lies in the possibility of its extension
to the more important -symmetric quantum field theory while the
other approaches which use complex contours are not willing to be applicable.
We calculated the effective potential of the massless theory as well
as the full spectrum of the theory. Although the calculations are carried out
up to first order in the coupling, the predicted spectrum is very close to the
exact one taken from other works. The most important result of this work is
that the effective potential obtained, which is equivalent to the Gaussian
effective potential, is bounded from below while the classical potential is
bounded from above. This explains the stability of the vacuum of the theory.
The obtained quasi-particle Hamiltonian is non-Hermitian but
-symmetric and we showed that the calculation of the metric
operator can go perturbatively. In fact, the calculation of the metric operator
can be done even for higher dimensions (quantum field theory) which, up till
now, can not be calculated in the other approaches either perturbatively or in
a closed form due to the possible appearance of field radicals. Moreover, we
argued that the effective theory is perturbative for the whole range of the
coupling constant and the perturbation series is expected to converge rapidly
(the effective coupling ).Comment: 14 pages, 5 figure
Possible treatment of the Ghost states in the Lee-Wick Standard Model
Very recently, the Lee-Wick standard model has been introduced as a non-SUSY
extension of the Standard model which solves the Hierarchy problem. In this
model, each field kinetic term attains a higher derivative term. Like any
Lee-Wick theory, this model suffers from existence of Ghost states. In this
work, we consider a prototype scalar field theory with its kinetic term has a
higher derivative term, which mimics the scalar sector in the Lee-Wick Standard
model. We introduced an imaginary auxiliary field to have an equivalent
non-Hermitian two-field scalar field theory. We were able to calculate the
positive definite metric operator in quantum mechanical and quantum
field versions of the theory in a closed form. While the Hamiltonian is
non-Hermitian in a Hilbert space with the Dirac sense inner product, it is
Hermitian in a Hilbert space endowed by the inner product as well
as having a correct-sign propagator (no Lee-Wick fields). Besides, the obtained
metric operator also diagonalizes the Hamiltonian in the two fields (no
mixing). Moreover, the Hermiticity of constrained the two Higgs masses
to be related as , which has been obtained in another work using a very
different regime and thus supports our calculation. Also, an equivalent
Hermitian (in the Dirac sense) Hamiltonian is obtained which has no Ghost
states at all, which is a forward step to make the Lee-Wick theories more
popular among the Physicists.Comment: 11 pages, 3 figure
Exact Critical Exponents of the Yang-Lee Model from Large-Order Parameters
Based on the Large-Order behavior of the perturbation series of the ground
state energy of Yang-Lee model we suggested a Hypergeometric approximants that
can mimic the same Large-order behavior of the given series. Near the branch
point, the Hypergeometric function has a power law behavior from
which the critical exponent and critical coupling can be extracted. While the
resummation algorithm shows almost exact predictions for the ground state
energy from law orders of perturbation series as input, we found that the exact
critical exponents are solely determined by one of the parameters in the large
order behavior of the series. Based on this result we conjecture that the
Large-order parameters might know the exact critical exponents. Since the
ground state energy is the generating functional of the 1-P irreducible
amplitudes, one gets all the critical exponents via functional differentiation
with respect to the external magnetic field.Comment: 13 pages, two table
- β¦