Related papers: Reply to arXiv:2203.14555
The identifications of transverse boost and rotation operators in light front theory done in Phys. Rev. Lett. {109}, 152005 (2012) is incorrect. The simple parton interpretation claimed is, in fact, for the transverse boost operator.…
We show the failure of a matricial version of Grothendieck's theorem for operator spaces, thereby resolving a long-standing open question in the field. Moreover, by showing that such a counterexample can occur in the simplest context of…
The aim of this short Note is to show that the Schr\"odinger and Heisenberg pictures of quantum mechanics are not equivalent unless one uses a quantization rule clearly stated by Born and Jordan in their famous 1925 paper. This rule is…
In biorthogonal quantum mechanics, the eigenvectors of a quasi-Hermitian operator and those of its adjoint are biorthogonal and complete and the probability for a transition from a quantum state to any one of these eigenvectors is positive…
It is shown that an arbitrary Fermion hopping hamiltonian can be represented by a system with no fermion fields, generalising earlier results by M. Levin & X.G. Wen [Phys Rev B 67, 245316 (2003)]. All the operators in the hamiltonian of…
We argue that our analysis of the J-Q model, presented in Phys. Rev. B 80, 174403 (2009), and based on a field-theory description of coupled dimers, captures properly the strong quantum fluctuations tendencies, and the objections outlined…
We show that the argument in Phys Rev Lett 70 (1993) 1360 is correct and consistent, and that Hagen & Sudarshan's solution has inconsistency leading to non-vanishing commutators of $[P^1, P^2]$ and $[P^j, H]$ even in physical states. This…
In a recent paper [ J. Stat. Mech. P07006 (2004)], E.G.D. Cohen and David Mauzerall (CM) have argued that the derivation of the nonequilibrium work relation given in [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] is flawed. Here I attempt…
In this article, we study the following question asked by Michael Hartz in a recent paper \cite{Hartz}: \textit{which operator spaces satisfy the column-row property?} We provide a complete classification of the column-row property for…
Canonical coordinates for both the Schroedinger and the nonlinear Schroedinger equations are introduced, making more transparent their Hamiltonian structures. It is shown that the Schroedinger equation, considered as a classical field…
This paper has been withdrawn by the author because overcame by arXiv:0910.4694
I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying pairs (A,B) of commuting nilpotent operators on a vector space contains the problem of classifying an arbitrary t-tuple of linear operators. Moreover, it contains…
We make a progress towards describing the semi-commutants of Toeplitz operators on Fock-Sobolev spaces of nonnegative orders. We generalize the results in \cite{Bauer1,Qin}. For the certain symbol spaces, we obtain two Toeplitz operators…
In a recent letter, Gaidarzhy et al. claim to have observed evidence for quantized displacements of a nanomechanical oscillator. We contend that the evidence, analysis, claims, and conclusions presented are contrary to expectations from…
We reply to the comments on our previous paper Physical Review Letters, Vol. 129, 087001 (2022), raised by Th\'eo S\'epulcre, Serge Florens, and Izak Snyman in arXiv:2210.00742.
In [JETP Lett. 105(3), 152 (2017)], a clear and comprehensive analysis of the paradoxical results of experiment [Phys. Rev. Lett. 111, 240402 (2013)] was carried out on the basis of the classical wave theory of light, which presupposes the…
In [Yu.M. Berezansky, E. Lytvynov, D. A. Mierzejewski, Ukrainian Math. J. 55 (2003), 853--858 ], the Jacobi field of a L\'evy process was derived. This field consists of commuting self-adjoint operators acting in an extended (interacting)…
This correspondence disproves the main results in the paper "Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection" by S. Mollaebrahim and B. Beferull-Lozano. Counterexamples and counterproofs are provided…
The flux of papers from electron positron colliders containing data on the photon structure function ended naturally around 2005. It is thus timely to review the theoretical basis and confront the predictions with a summary of the…
Marchildon's arguments against my earlier work are refuted.