Related papers: Dilatation operator or Hamiltonian?
On a static spacetime, the solutions of the Dirac equation are generated by a time-independent Hamiltonian. We study this Hamiltonian and characterize the split into positive and negative energy. We use it to find explicit expressions for…
Point splitting has been suggested as a way to deal with anomalous commutators in quantum field theory. It has been pointed out by D.G. Boulware[4] that in order to obtain a mathematically consistent theory the Hamiltonian operator must be…
In field theory the Poisson bracket $\{F, \mathcal{H}\}$ between an arbitrary function $F$ and the system Hamiltonian $\mathcal{H}$ acquires odd contributions. Here a modification is worked out to remove those terms, which leads to a…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
We explore aspects of dilation theory in the finite dimensional case and show that for a commuting $n$-tuple of operators $T=(T_1,...,T_n) $ acting on some finite dimensional Hilbert space $H$ and a compact set $X\subset \mathbb{C}^n$ the…
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…
A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d+1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outer boundary, is presented.
We discuss how to generalize a Dirac operator such that the solution of a Dirac equation is of bounded variation rather than continuous. We build the spectral theory for generalized Dirac operators and discuss the connection between them…
The interrelations between the two definitions of momentum operator, via the canonical energy-momentum tensorial operator and as translation operator (on the operator space), are studied in quantum field theory. These definitions give rise…
No bracket determines the evolution operator in covariant (polysymplectic and multisymplectic) Hamiltonian field theory.
We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach…
We show an equivalence between Dirac quantization and the reduced phase space quantization. The equivalence of the both quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are…
We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…
The Tomita-Takesaki modular operator for local algebras plays an important role in quantum field theory, and more recently in the study of relative entropy. However, the explicit expression of this operator, except for the case of wedges,…
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator $T$ can be dilated to a unitary $\cU$. A more general multivariable setting for these ideas is the setup where (i) the unit disk is replaced by a domain…
A field-theoretical space-time position operator can be properly introduced for the Dirac field, it plays the role of a generalized Noether charge associated with a local symmetry, and its second-quantized form shows that quantum fields…
We introduce and study the generalized Wigner operator. By definition, such an operator transforms the Wigner wave function into a local relativistic field corresponding to an irreducible representation of the Poincar\'e group by extended…
A novel expansion -- which generalizes Magnus expansion -- of the evolution operator associated with a (in general, time-dependent) perturbed Hamiltonian is introduced. It is shown that it has a wide range of possible solutions that can be…