Carl M. Bender, Gregorio Benincasa, Hugh F. Jones
In a recent Brief Report by Shalaby a new first-order perturbative calculation of the metric operator for an $iϕ^3$ scalar field theory is given. It is claimed that the result is an improvement on a previous calculation by Bender, Brody and Jones because it is local. Unfortunately Shalaby's calculation is not valid because of sign errors.
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This paper has been withdrawn by the author(s), due a mistake of factor 1/2.
A small comment on the paper with the mentioned title by Carl M. Bender, Dorje C. Brody and Hugh F. Jones.
In this report, we reply to a recent comment by Carl M. Bender, Gregorio Benincasa and Hugh F. Jones on our work 'New ansatz for metric operator calculation in pseudo-Hermitian field theory (Phys. Rev. D. 79, 107702 (2009)). In fact, they figured out that there exist sign errors in our work which leaded to the conclusion of the invalidity of the ansatz introduced in our work. Here, we show that, the ansatz is valid in d+1 space-time dimensions, which by itself is a new and very important result. The importance of the work comes from the fact that it is the first time to have a metric operator …
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 $ϕ$ and its conjugate field $π$ but also on the field gradient $\nablaϕ$. 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 $iϕ^{3}$ scalar field theory up to first order in the coupling. The higher orders can be conjectu…
We consider the Bethe Salpeter approach to the BFKL evolution in order to naturally incorporate the property of the Hermitian Separability in the BFKL approach. We combine the resulting all order ansatz for the BFKL eigenvalue together with reflection identities for harmonic sums and derive the most complicated term of the next-to-next-to-leading order BFKL eigenvalue in SUSY N=4. We also suggest a numerical technique for reconstructing the unknown functions in our ansatz from the known results for specific values of confomal spin.
We discuss the 't Hoof ansatz for instanton solutions in noncommutative U(2) Yang-Mills theory. We show that the extension of the ansatz leading to singular solutions in the commutative case, yields to non self-dual (or self-antidual) configurations in noncommutative space-time. A proposal leading to selfdual solutions with Q=1 topological charge (the equivalent of the regular BPST ansatz) can be engineered, but in that case the gauge field and the curvature are not Hermitian (although the resulting Lagrangian is real).
We demonstrate that the recent paper by Jana and Roy entitled ''Non-Hermitian quantum mechanics with minimal length uncertainty'' [SIGMA 5 (2009), 083, 7 pages, arXiv:0908.1755] contains various misconceptions. We compare with an analysis on the same topic carried out previously in our manuscript [arXiv:0907.5354]. In particular, we show that the metric operators computed for the deformed non-Hermitian Swanson models differs in both cases and is inconsistent in the former.
We explain why the main conclusion of Bender et al, hep-th/0511229 [J. Phys. A 39 (2006) 1657] regarding the practical superiority of the non-Hermitian description of PT-symmetric quantum systems over their Hermitian description is not valid. Recalling the essential role played by the Hermitian description in the characterization and interpretation of the physical observables, we maintain that as far as the physical aspects of the theory are concerned the Hermitian description is not only unavoidable but also indispensable.
Reply to the Comment on `The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'
本文回复Znojil对PT对称与准厄米量子理论操作基础的评论，澄清动机问题遭误解，说明文献取舍理由，并讨论标准量子理论扩展的可行约束与前景。
In a recent letter by Carl M. Bender and S. P. Klevansky [arXiv:1002.3253] an elementary field theory is proposed where the authors claimed that it can account for the existence of family of particles without any employment of group structures. In this work, we relied on the fact that the Dyson-Schwinger equations used by the authors stem from a variational principle and tried to reproduce their results by a mere variational algorithm. We were able to reproduce exactly their results by the employment of two different variational calculations of the vacuum energy in the proposed theory. We show…
We write the Hamiltonian for a gravitational spherically symmetric scalar field collapse with massive scalar field source, and we discuss the application of Wheeler De Witt equation as well as the appearence of time in this context. Using an Ansatz for Wheeler De Witt equation, solutions are discussed including the appearence of time evolution.
Following the recent proposal of Alday and Maldacena to obtain the strong coupling scattering amplitude in N=4 SYM via AdS/CFT, we point out that a unique solution can be obtained by imposing all the Virasoro constraints. In the case of four-gluon scattering, this solution is identical to the Alday-Maldacena solution, which is in accordance with the ansatz of Bern, Dixon and Smirnov. This also solves the moduli space problem of the four-point solution in a recent paper of Mironov, Morozov and Tomaras.
The unconstrained frame-like formulation of an infinite tower of completely symmetric tensor gauge fields is reviewed and examined in the limit where the cosmological constant goes to zero. By partially fixing the gauge and solving the torsion constraints, the form of the gauge transformations in the unconstrained metric-like formulation are obtained till first order in a weak field expansion. The algebra of the corresponding gauge symmetries is shown to be equivalent, at this order and modulo (unphysical) gauge parameter redefinitions, to the Lie algebra of Hermitian differential operators on…
The S-matrix Ansatz has been proposed by 't Hooft to overcome difficulties and apparent contradictions of standard quantum field theory close to the black hole horizon. In this paper we revisit and explore some of its aspects. We start by computing gravitational backreaction effects on the properties of the Hawking radiation and explain why a more powerful formalism is needed to encode them. We then use the map bulk-boundary fields to investigate the nature of exchange algebras satisfied by operators associated with ingoing and outgoing matter. We propose and comment on some analogies between …
We study boundary bound states using the Bethe ansatz formalism for the finite $XXZ$ $(Δ>1)$ chain in a boundary magnetic field $h$. Boundary bound states are represented by the ``boundary strings'' similar to those described in the work of H.Saleur, S.Skorik. We find that for certain values of $h$ the ground state wave function contains boundary strings, and from this infer the existence of two ``critical'' fields in agreement with the results of Jimbo et al. An expression for the vacuum surface energy in the thermodynamic limit is derived and found to be an analytic function of $h$. We argue…
Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schrodinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators.
Recently, Hata and Kojita proposed a new energy formula for a class of solutions in Witten's open string field theory based on a novel symmetry of correlation functions they found. Their energy formula can be regarded as a generalization of the conventional energy formula by Murata and Schnabl. Following their proposal, we investigate their new ansatz for the classical solution representing double D-branes. We present a regularized definition of this solution and show that the solution satisfies the equation of motion when it is contracted with the solution itself and when it is contracted wit…
The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a recurrence relation. The commutation relations between the generating function t(λ) of the integrals of motion and the creation operators are calculated and therefore the algebraic Bethe Ansatz is fully implemented. The energy spectrum as well as the corresponding Bethe equations of the system coincide with the ones of the sl_2-invariant Gaudin model. As opposed…
We address some issues related to the construction of general Kaluza-Klein (KK) ansätze for the compactification of a supergravity (sugra) theory on a sphere $S_m$. We first reproduce various ansätze for compactification to 7d from the ansatz for the full nonlinear KK reduction of 11d sugra on $AdS_7\times S_4$. As a side result, we obtain a lagrangian formulation of 7d ${\cal N}=2$ gauged sugra, which so far had only a on-shell formulation, through field equations and constraints. The $AdS_7\times S_4$ ansatz generalizes therefore all previous sphere compactifications to 7d. Then we consider …
Self-duality and the Holomorphic Ansatz in Generalized BPS Skyrme Model
本文将 BPS Skyrme 模型推广到简单紧李群对应的厄米对称空间，并利用推广的全纯映射拟设构造了无穷多个精确自对偶 Skyrmion 解，揭示了矩阵场 h 的自由度随群维数增长。
We perform a perturbative calculation of the physical observables, in particular pseudo-Hermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator, and the classical Hamiltonian for the PT-symmetric cubic anharmonic oscillator, $ H=p^1/(2m)+μ^2x^2/2+iεx^3 $. Ignoring terms of order $ ε^4 $ and higher, we show that this system describes an ordinary quartic anharmonic oscillator with a position-dependent mass and real and positive coupling constants. This observation elucidates the classical origin of the reality and positivity of the energy spectrum. We also discus…
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