Mixing and oscillations of neutral particles in Quantum Field Theory

We study the mixing of neutral particles in Quantum Field Theory: neutral boson field and Majorana field are treated in the case of mixing among two generations. We derive the orthogonality of flavor and mass representations and show how to consistently calculate oscillation formulas, which agree with previous results for charged fields and exhibit corrections with respect to the usual quantum mechanical expressions.Comment: 8 pages, revised versio

Quantisation of twistor theory by cocycle twist

We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra form which we can then `quantise' by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor space CP^3, compactified Minkowski space CMh and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the formulation in terms of projective varieties. We outline how the Penrose-Ward transform then quantises. As an example, we show that the pull-back of the tautological bundle on CMh pulls back to the basic instanton on S^4\subset CMh and that this observation quantises to obtain the Connes-Landi instanton on \theta-deformed S^4 as the pull-back of the tautological bundle on our \theta-deformed CMh. We likewise quantise the fibration CP^3--> S^4 and use it to construct the bundle on \theta-deformed CP^3 that maps over under the transform to the \theta-deformed instanton.Comment: 68 pages 0 figures. Significant revision now has detailed formulae for classical and quantum CP^

Quantum Field Theory of three flavor neutrino mixing and oscillations with CP violation

We study in detail the Quantum Field Theory of mixing among three generations of Dirac fermions (neutrinos). We construct the Hilbert space for the flavor fields and determine the generators of the mixing transformations. By use of these generators, we recover all the known parameterizations of the three-flavor mixing matrix and we find a number of new ones. The algebra of the currents associated with the mixing transformations is shown to be a deformed $su(3)$ algebra, when CP violating phases are present. We then derive the exact oscillation formulas, exhibiting new features with respect to the usual ones. CP and T violation are also discussed.Comment: 15 pages, 7 figures, RevTeX, revised versio

Bounding and unbounding higher extensions for SL2

We analyse the recursive formula found for various Ext groups for SL2(k)SL2(k), k a field of characteristic p , and derive various generating functions for these groups. We use this to show that the growth rate for the cohomology of SL2(k)SL2(k) is at least exponential. In particular, View the MathML sourcemax{dimExtSL2(k)i(k,Δ(a))|a,i∈N} has (at least) exponential growth for all p . We also show that View the MathML sourcemax{dimExtSL2(k)i(k,Δ(a))|a∈N} for a fixed i is bounded

An introduction to quantum mechanics

SIGLEAvailable from British Library Document Supply Centre- DSC:q89/08921(Introduction) / BLDSC - British Library Document Supply CentreGBUnited Kingdo