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If one studies the canonical commutation relations (CCR's) of quantum field theory in the unitary Weyl form, one does not know if one can find a common dense domain for the field operators since their domain of definition depends on the test function. We consider here a general class of test...
The (ϕ 2 ) s +1 quantum field theory model can be solved exactly, where the number of space dimensions is s ≤ 3. Thus this model explicitly illustrates many properties of nontrivial models such as (ϕ 2 n ) 2 and Yukawa 2 . In particular we study hyperbolicity, the energy spectrum, local...
Certain differential‐geometric and Lie group theoretic facts that are useful in the systematic study and search for spectrum generating algebras are presented.
A new method is proposed for constructing examples in relativistic classical particle mechanics, starting with the Poincaré group and space reflections as transformations of position and velocity variables for two free particles and deriving equations for Lorentz covariant position variables for...
All tensors of contravariant valency two, which are divergence free on one index and which are concomitants of the metric tensor, together with its first two derivatives, are constructed in the four‐dimensional case. The Einstein and metric tensors are the only possibilities.
A prescription is given for obtaining the Green's function for N free particles which can have different masses. The approach is systematic and straightforward. A coordinate transformation of the Fourier integral representation of the N ‐particle noninteracting Green's function facilitates the...
Scattering by a short‐range potential is described by the wavefunction ψ having the asymptotic form Ψ→ e i k ⋅ r + F e i k r , r →∞, Ψ → e i k ⋅ r + F e i k r , r → ∞ , where F F has the series representation F = f ( k , k r )/ r + g ( k , k r )/ r 2 +…. F = f ( k , k r )...
We prove that solutions to the equations Γ j k ; l i = 0 and g i j ; k = 0 Γ j k ; l i = 0 and g i j ; k = 0 exist locally when R j k l i ≠ 0 R j k l i ≠ 0 . Previously this was only shown for the special case of R j k l i = 0 R j k l i = 0 .
We determine entirely the n ‐body nonlocal potentials, parameters of a given Lagrangian field theory, in terms of a set of independent functionals of the many‐body propagators. These functionals are more suitable for the description of self‐generating interactions than the many‐body...
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