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• 1965-1969  (334)
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• 1
Electronic Resource
Springer
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract Dyson's power counting theorem is proved for the case of Minkowski metric.
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• 2
Electronic Resource
Springer
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract A study is made of the relationship ofS U 3 and its adjoint groupS U3/Z3 to the subgroup ofR8 which leaves invariant not only the lengtha i a i of a real eight component vectora i but also the cubic invariantd i j k a i a j a k ,d i j k being the totally symmetric isotropicS U3 tensor introduced byGell-Mann. A formula for the rotationR ε R8 corresponding toU ε S U3, and a formula inverse to this, which provides a way of parametrizingU ε S U3, are derived.
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• 3
Electronic Resource
Springer
Communications in mathematical physics 11 (1968), S. 125-130
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract Necessary conditions are given for the TCP invariance of a local field with usual energy-momentum spectrum. Examples are constructed of both Fermi and Bose local free infinite-component fields which violate these conditions and consequently do not allow a TCP symmetry.
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• 4
Electronic Resource
Springer
Communications in mathematical physics 11 (1968), S. 131-137
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract The problem of the combined space-time and internal symmetry of elementary Particles is investigated from the view-point of the Lie algebras deformation theory. It is demonstrated that the deformations of the direct sum of the Poincaré and internal symmetry algebras conserve the structure of the direct sum, if the internal symmetry is semi-simple or is described by the special type of algebras with abelian ideal. So the internal and space-time characteristics of the system remain independent.
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• 5
Electronic Resource
Springer
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract Our most complete results concern the Ising spin system with purely ferromagnetic interactions in a magnetic fieldH (or the corresponding lattice gas model with fugacityz=const. exp(−2mHβ) wherem is the magnetic moment of each spin). We show that, in the limit of an infinite lattice, (i) the free energy per site and the distribution functionsn s (x 1, ...,x s ; β,z) are analytic in the two variables β andH if the reciprocal temperature β〉0 and the complex numberH is not a limit point of zeros of the grand partition function ξ, and (ii) the Ursell functionsu s (x 1, ...,x s ; β,z) tend to 0 as Δ s ≡Max i, j |x i −x j | → ∞ if β〉0 and ReH≠0; in particular, if the interaction potential vanishes for separations exceeding some fixed cutoff value λ, then |u s |〈C exp [(−2 βm |ReH|+ε) Δ s /λ] where ε is any small positive number andC is independent of Δ s . One consequence of the result (i) is that a phase transition can occur as β is varied at constantH only ifH is a limit point of zeros of ξ (which can happen only if ReH=0); this supplements Lee and Yang's result that the same condition is necessary for a phase transition whenH is varied at constant β. For a lattice or continuum gas with non-negative interaction potential (corresponding, in the lattice case, to an Ising antiferromagnet), similar results are shown to hold provided β〉0 and the complex fugacityz is less than the radius of convergence of the Mayerz expansion; for the continuum gas, however,n s andu s must be replaced by their values integrated over small volumes surrounding each of the pointsx 2, ...,x s . It is shown that the pressurep is analytic in both β andz, if it is analytic inz at fixed β over a suitable range of values of β andz, and further that, except for continuum systems without hard cores,p,n s andu s have convergent Maclaurin expansions in β for small enoughz.
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• 6
Electronic Resource
Springer
Communications in mathematical physics 11 (1968), S. 168-180
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract In the theory of line breadth phenomena excited amplitudes must not exactly follow the usual exponential decay law. This fact is well known from fundamental mathematical considerations, although there is not any unique form for the corresponding deviation. In this paper we seek a new expression for the decay, based upon a rather general field model of mass zero. The result is a good approximation for times ≈ 1/γ and yields the exact asymptotic solution. A modification to a model with mass ≠0 does not in general lead to other formulations of the solution.
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• 7
Electronic Resource
Springer
Communications in mathematical physics 11 (1969), S. 181-182
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
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• 8
Electronic Resource
Springer
Communications in mathematical physics 11 (1968), S. 138-167
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract Taking into account the fact that space groups are groups of transformations of Euclideann-dimensional space, non-equivalent systems of non-primitive translations are defined. They can be brought into one-to-one correspondence with the elements of the groupH 1 (K, R n /Z n ) or with those of the groupH 1 (K, Z n /kZ n )/H 1 (K, Z n ). (K is a point group of orderk.) The consistency of these findings with the results of Part I is given by the isomorphisms \$\$H^2 (K,Z^n ) \cong H^1 (K,R^n /Z^n ) \cong H^1 (K,Z^n /kZ^n )/H^1 (K,Z^n ).\$\$ Theorems are proved giving the conditions for cohomology groupsH q (K, A) to be zero. These conditions are fulfilled in particular ifA=R n andK is a subgroup ofGL (n, R) that either is compact (thenq〉0) or has a finite normal subgroup leaving no element ofR n invariant (thenq≧0). This implies that the affine, the Euclidean and the inhomogeneous Lorentz groups are the only extensions ofR n by the corresponding homogeneous groups. By way of illustration, the theory of this paper is applied to two 2-dimensional space groups.
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• 9
Electronic Resource
Springer
Communications in mathematical physics 11 (1969), S. 183-197
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract A sufficient condition is given in order that a von Neumann algebra with cyclic vector is quasi-standard. With the help of this result it is proved that a locally normal state with a cyclic and separating vector in the representation space gives rise to a quasi-standard von Neumann algebra. Furthermore it is proved that the representation space determined by a locally normal state in the G.N.S. construction is separable.
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• 10
Electronic Resource
Springer
Communications in mathematical physics 11 (1969), S. 198-213
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract The Green functions of the anisotropic Heisenberg model are studied by a method which was applied previously to the reduced density matrices. Integral equations are used to prove the existence of the infinite volume limit of the Green functions, and some analyticity properties with respect to the fugacity (or magnetic field), the potentials, and the complex times.
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