8 research outputs found
q-Deformed Relativistic Wave Equations
Based on the representation theory of the -deformed Lorentz and Poincar\'e
symmeties -deformed relativistic wave equation are constructed. The most
important cases of the Dirac-, Proca-, Rarita-Schwinger- and Maxwell- equations
are treated explicitly. The -deformed wave operators look structurally like
the undeformed ones but they consist of the generators of a non-commu\-ta\-tive
Minkowski space. The existence of the -deformed wave equations together with
previous existence of the -deformed wave equations together with previous
results on the representation theory of the -deformed Poincar\'e symmetry
solve the -deformed relativistic one particle problem.Comment: 17 Page
Exact two-particle Matrix Elements in S-Matrix Preserving Deformation of Integrable QFTs
In a recent paper it was shown that the response of an integrable QFT under
variation of the Unruh temperature can be computed from a S-matrix preserving
deformation of the form factor approach. We give explicit expressions for the
deformed two-particle formfactors for various integrable models: The
Sine-Gordon and SU(2) Thirring model, several perturbed minimal CFTs and the
real coupling affine Toda series. A uniform pattern is found to emerge when
both the S-matrix and the deformed form factors are expressed in terms Barnes'
multi-periodic functions.Comment: 9 pages, Latex, no figure
Replica-deformation of the SU(2)-invariant Thirring model via solutions of the qKZ equation
The response of an integrable QFT under variation of the Unruh temperature
has recently been shown to be computable from an S-matrix preserving
(`replica') deformation of the form factor approach. We show that
replica-deformed form factors of the SU(2)-invariant Thirring model can be
found among the solutions of the rational -type quantum
Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved
charge solutions the deformed form factors are in one-to-one correspondence to
the ones at level zero and use this to conjecture the deformed form factors of
the Noether current in our model.Comment: 30 pages, Latex, Dedicated to Moshe Flat
On the deformability of Heisenberg algebras
Based on the vanishing of the second Hochschild cohomology group of the
enveloping algebra of the Heisenberg algebra it is shown that differential
algebras coming from quantum groups do not provide a non-trivial deformation of
quantum mechanics. For the case of a q-oscillator there exists a deforming map
to the classical algebra. It is shown that the differential calculus on quantum
planes with involution, i.e. if one works in position-momentum realization, can
be mapped on a q-difference calculus on a commutative real space. Although this
calculus leads to an interesting discretization it is proved that it can be
realized by generators of the undeformed algebra and does not posess a proper
group of global transformations.Comment: 16 pages, latex, no figure
Selfdual 2-form formulation of gravity and classification of energy-momentum tensors
It is shown how the different irreducibility classes of the energy-momentum
tensor allow for a Lagrangian formulation of the gravity-matter system using a
selfdual 2-form as a basic variable. It is pointed out what kind of
difficulties arise when attempting to construct a pure spin-connection
formulation of the gravity-matter system. Ambiguities in the formulation
especially concerning the need for constraints are clarified.Comment: title changed, extended versio