Related papers: Spin and Statistics in Galilean Covariant Field Th…
A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…
A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation…
The second central extension of the planar Galilei group has been alleged to have its origin in the spin variable. This idea is explored here by considering local Galilean covariant field theory for free fields of arbitrary spin. It is…
Coordinate scaling of each spin density separately is considered in spin density functional theory. A virial theorem relates the spin-scaled correlation energy to the spin-scaled correlation potentials. An adiabatic connection formula…
We reexamine the connection between spin and statistics through the quantization of a complex scalar field, using the formulation with the property that the hermitian conjugate of canonical momentum for a variable is just the canonical…
In a recent paper, algebraic descriptions for all non-relativistic spins were derived by elementary means directly from the Lie algebra $\specialorthogonalliealgebra{3}$, and a connection between spin and the geometry of Euclidean…
It is well-known that is spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing…
We investigate the intrinsic reason for spin statistics connection. It is found that if a free field theory is rotationally (SU(2)) invariant, and has time reversal ($T$) and charge conjugation ($C$) symmetries, it obeys the spin statistics…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
These notes are devoted to the intriguing and still largely unexplored links between String Theory and Higher Spins, the types of excitations that lie behind its most cherished properties. A closer look at higher-spin fields provides some…
It has been known for some time that topological geons in quantum gravity may lead to a complete violation of the canonical spin-statistics relation : there may exist no connection between spin and statistics for a pair of geons. We present…
These notes comprise a part of the introductory lectures on Higher Spin Theory presented in the Eighth Modave Summer School in Mathematical Physics. We construct free higher-spin theories and turn on interactions to find that…
The statistics of soliton sectors of massive 2D field theories is analysed. In the soliton field algebra, the non-local commutation relations are determined and Weak Locality, Spin-Statistics and CPT theorems are proven. These theorems…
New developments on the symmetries of non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a…
A necessary and sufficient condition for Pauli's spin-statistics relation is given for nonrelativistic anyons, bosons, and fermions in two and three spatial dimensions. For any point particle species in two spatial dimensions, denote by J…
In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation…
A covariant calculus for the construction of effective string theories is developed. Effective string theory, describing quantum string-like excitations in arbitrary dimension, has in the past been constructed using the principles of…
We point out that the existence of global symmetries in a field theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a field theory…
These lectures were given in the framework of the ``Dixi\`eme s\'eminaire rhodanien de physique'' entitled ``Le spin en physique'', given at Villa Gualino, Turin, March 2002. We have shown how the difficulties of interpretation of atomic…
The twist-deformation of the Poincar\'e algebra as symmetry of the field theories on noncommutative space-time with Heisenberg-like commutation relation is discussed in connection to the relation between a sound approach to the twist and…