The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

GABAa Receptor Mediated Signalling in the Brain: Inhibition, Shunting and Excitation

Within central nervous system, the simple division of chemical synaptic transmission to depolarizing excitation mediated by glutamate and hyperpolarizing inhibition mediated by γ-amino butyric acid (GABA), is evidently an oversimplification. The GABAa receptor (GABAaR) mediated responses can be of opposite sign within a single resting cell, due to the compartmentalized distribution of cation chloride cotransporters (CCCs). The K+/Cl- cotransporter 2 (KCC2), member of the CCC family, promotes K+ fuelled Cl- extrusion and sets the reversal potential of GABA evoked anion currents typically slightly below the resting membrane potential. The interesting ionic plasticity property of GABAergic signalling emerges from the short-term and long-term alterations in the intraneuronal concentrations of GABAaR permeable anions (Cl- and HCO3-). The short-term effects arise rapidly (in the time scale of hundreds of milliseconds) and are due to the GABAaR activation dependent shifts in anion gradients, whereas the changes in expression, distribution and kinetic regulation of CCCs are underlying the long-term effects, which may take minutes or even hours to develop. In this Thesis, the differences in the reversal potential of GABAaR mediated responses between dopaminergic and GABAergic cell types, located in the substantia nigra, were shown to be attributable to the differences in the chloride extrusion mechanisms. The stronger inhibitory effect of GABA on GABAergic neurons was due to the cell type specific expression of KCC2 whereas the KCC2 was absent from dopaminergic neurons, leading to a less prominent inhibition brought by GABAaR activation. The levels of KCC2 protein exhibited activity dependent alterations in hippocampal pyramidal neurons. Intense neuronal activity, leading to a massive release of brain derived neurotrophic factor (BDNF) in vivo, or applications of tyrosine receptor kinase B (TrkB) agonists BDNF or neurotrophin-4 in vitro, were shown to down-regulate KCC2 protein levels which led to a reduction in the efficacy of Cl- extrusion. The GABAergic transmission is interestingly involved in an increase of extracellular K+ concentration. A substantial increase in interstitial K+ tends to depolarize the cell membrane. The effects that varying ion gradients had on the generation of biphasic GABAaR mediated responses were addressed, with particular emphasis on the novel idea that the K+/Cl- extrusion via KCC2 is accelerated in response to a rapid accumulation of intracellular Cl-. The KCC2 inhibitor furosemide produced a large reduction in the GABAaR dependent extracellular K+ transients. Thus, paradoxically, both the inefficient KCC2 activity (via increased intracellular Cl-) and efficient KCC2 activity (via increased extracellular K+) may promote excitation.

Spin and relativistic motion of bound states

The wave functions of moving bound states may be expected to contract in the direction of motion, in analogy to a rigid rod in classical special relativity, when the constituents are at equal (ordinary) time. Indeed, the Lorentz contraction of wave functions is often appealed to in qualitative discussions. However, only few field theory studies exist of equal-time wave functions in motion. In this thesis I use the Bethe-Salpeter formalism to study the wave function of a weakly bound state such as a hydrogen atom or positronium in a general frame. The wave function of the e^-e^+ component of positronium indeed turns out to Lorentz contract both in 1+1 and in 3+1 dimensional quantum electrodynamics, whereas the next-to-leading e^-e^+\gamma Fock component of the 3+1 dimensional theory deviates from classical contraction. The second topic of this thesis concerns single spin asymmetries measured in scattering on polarized bound states. Such spin asymmetries have so far mainly been analyzed using the twist expansion of perturbative QCD. I note that QCD vacuum effects may give rise to a helicity flip in the soft rescattering of the struck quark, and that this would cause a nonvanishing spin asymmetry in \ell p^\uparrow -> \ell' + \pi + X in the Bjorken limit. An analogous asymmetry may arise in p p^\uparrow -> \pi + X from Pomeron-Odderon interference, if the Odderon has a helicity-flip coupling. Finally, I study the possibility that the large single spin asymmetry observed in p p^\uparrow -> \pi(x_F,k_\perp) + X when the pion carries a high momentum fraction x_F of the polarized proton momentum arises from coherent effects involving the entire polarized bound state.

Experimental approach for studying structural changes in axonal membrane upon nerve excitation

The Hodgkin and Huxley (HH) model of action potential has become a central paradigm of neuroscience. Despite its ability to predict action potentials with remarkable accuracy, it fails to explain several biophysical findings related to the initiation and propagation of the nerve impulse. The isentropic heat release and optical phenomena demonstrated by various experiments suggest that action potential is accompanied by a transient phase change in the axonal membrane. In this study a method was developed for preparing a giant axon from the crayfish abdominal cord for studying the molecular mechanisms of action potential simultaneously by electrophysiological and optical methods. Also an alternative setup using a single-cell culture of an Aplysia sensory neuron is presented. In addition to the description of the method, the preliminary results on the effect of phloretin, a dipole potential lowering compound, on the excitability of a crayfish giant axon are presented.