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Spheres with more than 7 vector fields: all the fault of Spin(9)
Spin(9) octonions vector fields on spheres
2011/8/24
Abstract: We give an interpretation in terms of the Lie group Spin(9) of the maximal number of linearly independent vector fields on odd dimensional spheres.
Hilbert's Tenth Problem and Mazur's Conjectures in Complementary Subrings of Number Fields
Hilbert’s Tenth Problem undecidability elliptic curves primitive divisor
2011/2/24
We show that Hilbert’s Tenth Problem is undecidable for complementary subrings of number fields and that the p-adic and archimedean ring versions of Mazur’s conjectures do not hold in these rings .
Central limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition
Central limit theorems Hilbert-space valued
2011/1/19
In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced ρ′-mixing condition.
Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes
Approximate KMS scala spinor fields Friedmann-Robertson-Walker spacetimes
2010/12/16
We construct and discuss Hadamard states for both scalar and Dirac spinor fields in a large
class of spatially flat Friedmann-Robertson-Walker spacetimes characterised by an initial phase either of e...
Nontrivial realization of the space-time translations in the theory of quantum fields
Nontrivial realization of the space-time translations theory of quantum fields
2010/12/15
In standard quantum field theory, the one–particle states are classified by unitary epresentations of the Poincar´e group, whereas the causal fields’ classification employs the finite dimensiona...
Covariant Quantum Fields on Noncommutative Spacetimes
Covariant Quantum Fields Noncommutative Spacetimes
2010/12/16
A spinless covariant field ϕ on Minkowski spacetime Md+1 obeys the relation U(a,)ϕ(x)U(a,)−1 =ϕ(x + a) where (a,) is an element of the Poincar´e group P↑ + and U : (a,)...