<p>The appearance in string theory of higher-dimensional objects known as D-branes has been a source of much of the interesting developements in the subject during the past ten years. A very interesting phenomenon occurs when several of these D-branes are made to coincide: The abelian gauge theory living on each brane is enhanced to a non-abelian gauge theory living on the stack of coincident branes. This gives rise to interesting effects like the natural appearance of non-commutative geometry. The theory governing the dynamics of these coincident branes is still poorly understood however and only hints of the underlying structure have been seen.</p><p>This thesis focuses on an attempt to better this understanding by writing down actions for coincident branes using so-called boundary fermions, originating in considerations of open strings, instead of matrices to describe the non-abelian fields. It is shown that by gauge-fixing and by suitably quantizing these boundary fermions the non-abelian action that is known, the Myers action, can be reproduced. Furthermore it is shown that under natural assumptions, unlike the Myers action, the action formulated using boundary fermions also posseses kappa-symmetry, the criterion for being the correct supersymmetric action for coincident D-branes.</p><p>Another aspect of string theory discussed in this thesis is that of tensionless strings. These are of great interest for example because of their possible relation to higher spin gauge theories via the AdS/CFT-correspondence. The tensionless superstring in a plane wave background, arising as a particular limit of the near-horizon geometry of a stack of D3-branes, is considered and compared to the tensile case.</p>

The appearance in string theory of higher-dimensional objects known as D-branes has been a source of much of the interesting developements in the subject during the past ten years. A very interesting phenomenon occurs when several of these D-branes are made to coincide: The abelian gauge theory living on each brane is enhanced to a non-abelian gauge theory living on the stack of coincident branes. This gives rise to interesting effects like the natural appearance of non-commutative geometry. The theory governing the dynamics of these coincident branes is still poorly understood however and only hints of the underlying structure have been seen. This thesis focuses on an attempt to better this understanding by writing down actions for coincident branes using so-called boundary fermions, originating in considerations of open strings, instead of matrices to describe the non-abelian fields. It is shown that by gauge-fixing and by suitably quantizing these boundary fermions the non-abelian action that is known, the Myers action, can be reproduced. Furthermore it is shown that under natural assumptions, unlike the Myers action, the action formulated using boundary fermions also posseses kappa-symmetry, the criterion for being the correct supersymmetric action for coincident D-branes. Another aspect of string theory discussed in this thesis is that of tensionless strings. These are of great interest for example because of their possible relation to higher spin gauge theories via the AdS/CFT-correspondence. The tensionless superstring in a plane wave background, arising as a particular limit of the near-horizon geometry of a stack of D3-branes, is considered and compared to the tensile case.

This thesis studies U(1) Chern-Simons theory and its relation to the results of Chris Beasley and Edward Witten (2005). Using the partition function formalism, we are led to compare U(1) Chern-Simons theory as constructed by Manoliu (1998) to the results of Beasley and Witten (2005). This leads to an explicit calculation of the U(1) Chern Simons partition function on a closed Sasakian three-manifold and opens the door to studying rigorous extensions of this theory to more general gauge groups and three-manifold geometries.

The Higgs boson has an important role in the theoretical formulation of the standard model of fundamental interactions. Symmetry breaking of the vacuum via the Higgs field allows the gauge bosons of the weak interaction and all fermions to acquire mass in a way that preserves gauge-invariance, and thus renormalizablility. The Standard Model can accommodate an arbitrary number of Higgs fields with appropriate charge assignments. To explore the effects of multiple Higgs particles, the SU(2)-multi-Higgs model is studied using lattice simulations, a non-perturbative technique in which the fields are placed on a discrete space-time lattice. The formalism and methods of lattice field theory are discussed in detail. Standard results for the SU(2)-Higgs model are reproduced via Monte Carlo simulations, in particular the single-Higgs phase structure, which has a region of analytic connection between the symmetric and Higgs phases. The phase structure of the SU(2)-multi-Higgs model is explored for the case of N >= 2 identical Higgs fields. There is no remaining region of analytic connection between the phases, at least when interactions between different Higgs flavours are omitted. An explanation of this result in terms of enhancement from overlapping phase transitions is explored for N = 2 by introducing an asymmetry in the hopping parameters of the Higgs fields.

This thesis studies U(1) Chern-Simons theory and its relation to the results of Chris Beasley and Edward Witten (2005). Using the partition function formalism, we are led to compare U(1) Chern-Simons theory as constructed by Manoliu (1998) to the results of Beasley and Witten (2005). This leads to an explicit calculation of the U(1) Chern Simons partition function on a closed Sasakian three-manifold and opens the door to studying rigorous extensions of this theory to more general gauge groups and three-manifold geometries.

The Higgs boson has an important role in the theoretical formulation of the standard model of fundamental interactions. Symmetry breaking of the vacuum via the Higgs field allows the gauge bosons of the weak interaction and all fermions to acquire mass in a way that preserves gauge-invariance, and thus renormalizablility. The Standard Model can accommodate an arbitrary number of Higgs fields with appropriate charge assignments. To explore the effects of multiple Higgs particles, the SU(2)-multi-Higgs model is studied using lattice simulations, a non-perturbative technique in which the fields are placed on a discrete space-time lattice. The formalism and methods of lattice field theory are discussed in detail. Standard results for the SU(2)-Higgs model are reproduced via Monte Carlo simulations, in particular the single-Higgs phase structure, which has a region of analytic connection between the symmetric and Higgs phases. The phase structure of the SU(2)-multi-Higgs model is explored for the case of N >= 2 identical Higgs fields. There is no remaining region of analytic connection between the phases, at least when interactions between different Higgs flavours are omitted. An explanation of this result in terms of enhancement from overlapping phase transitions is explored for N = 2 by introducing an asymmetry in the hopping parameters of the Higgs fields.

<p>In this thesis, we study effective field theories for doubly heavy baryons and lattice QCD. We construct a chiral Lagrangian for doubly heavy baryons and heavy mesons that is invariant under heavy quark-diquark symmetry at leading order and includes the leading O(1/m_Q ) symmetry violating operators. The theory is used to predict the electromagnetic decay width of the J = 3/2 member of the ground state doubly heavy baryon doublet. Numerical estimates are provided for doubly charm baryons. We also calculate chiral corrections to doubly heavy baryon masses and strong decay widths of low lying excited doubly heavy baryons. We derive the couplings of heavy diquarks to weak currents in the limit of heavy quark-diquark symmetry, and construct the chiral Lagrangian for doubly heavy baryons coupled to weak currents. Chiral corrections to doubly heavy baryon zero-recoil semileptonic decay for both unquenched and partially quenched QCD are calculated. This theory is used to derive chiral extrapolation formulae for measurements of the doubly heavy baryon zero-recoil semileptonic decay form factors in lattice QCD simulations. Additionally, we study the pion physics on lattice using chiral perturbation theory. For finite volume field theories with discrete translational invariance, conserved currents can obtain additional corrections from infrared effects. We demonstrate this for pions using chiral perturbation theory coupled to electromagnetism in a periodic box. Gauge invariant single particle effective theories are constructed to explain these results. We use chiral perturbation theory to study the extraction of pion electromagnetic polarizabilities from lattice QCD. Chiral extrapolation formulae are derived for partially quenched and quenched QCD simulations. We determine finite volume corrections to the Compton scattering tensor of pions.</p> / Dissertation

Η μεταπτυχιακή μου εργασία χωρίζεται σε δύο μέρη: Στο Πρώτο μέρος γίνεται μια σύντομη αναφορά στις θεμελιώδεις αρχές της Κβαντομηχανικής και μια ιστορική αναδρομή στους Φυσικούς και Μαθηματικούς που έβαλαν ο καθένας το δικό τους λιθαράκι για να φθάσουμε στο σήμερα και στην ανακάλυψη του σωματιδίου Higgs. Συγχρόνως γίνεται και μια εννοιολογική αναδρομή που περιγράφει τα όρια και τα περιεχόμενα της Σύγχρονης Φυσικής στην οποία περιέχεται η κβαντική θεωρία καθώς και η σχέση της με την Κλασική Φυσική. Το Δεύτερο μέρος με την σειρά του χωρίζεται σε πέντε κεφάλαια: Στο πρώτο κεφάλαιο δίνονται οι σχετικιστικές εξισώσεις Klein-Gordon και Dirac εξηγώντας τα προβλήματα που λύνει και τα εμπόδια που αντιμετωπίζει η κάθε μια τους. Στο δεύτερο κεφάλαιο γίνεται αναφορά στην θεωρία πεδίων ως λύση των προβλημάτων που δημιουργούν οι εξισώσεις του πρώτου κεφαλαίου. Συνεχίζει με την μελέτη του θεωρήματος της Noether και τις συνέπειές του στην Φυσική καθώς επίσης και με την κβάντωση των κλασικών πεδίων. Πιο συγκεκριμένα, δίνονται οι έννοιες της κανονικής κβάντωσης, εξετάζεται το πραγματικό και μιγαδικό πεδίο Klein-Gordon όπως και τα κβαντισμένα πεδία Dirac και Schrodinger. Το δεύτερο κεφάλαιο κλείνει με το κβαντισμένο ηλεκτρομαγνητικό πεδίο. Στο τρίτο κεφάλαιο γίνεται μια αναφορά σε Lie-ομάδες και άλγεβρες Lie όπως και στις ομάδες SU(2) και SU(3). Για την παρουσίαση της θεωρίας των ομάδων Lie αναφέρονται κάποιοι ορισμοί, προτάσεις και μικρά παραδείγματα. Το τέταρτο κεφάλαιο ασχολείται με τις θεωρίες βαθμίδας, με τους παγκόσμιους και τοπικούς μετασχηματισμούς στο πραγματικό και μιγαδικό πεδίο Klein-Gordon, με το πεδίο Yang-Mills και την θεωρία ενοποίησης. Στο πέμπτο κεφάλαιο κυριαρχεί το αυθόρμητο σπάσιμο συμμετρίας, με το θεώρημα Goldstone και κυρίως με τον μηχανισμό Higgs εξηγώντας πως τα μποζόνια βαθμίδας του Καθιερωμένου Προτύπου αποκτούν μάζα. / My Master's thesis consists of two parts: In the first part there is a brief reference regarding the fundamental principles of Quantum Mechanics and a historical retrospection of how physicists and mathematicians each made their own contribution in order for us today to reach to the discovery of the Higgs particle. In parallel, there is a conceptual overview that describes the boundaries and contents of Modern Physics, which includes Quantum Theory and its relation to Classical Physics. In the second part there are five chapters: The first chapter describes the Klein-Gordon and Dirac relativistic equations, explaining the advantages and drawbacks that each of them have. The second chapter refers to the field theory as a solution to the problems posed by the equations of the first chapter. It continues with a study of the Noether theorem and its consequences in Physics, as well as the quantization of classical fields. In particular, the concepts of normal quantization are given out, the real and the complex field of Klein- Gordon is examined, as well as the quantized Dirac and Schrodinger fields. It ends with the quantized electromagnetic field. The third chapter describes the Lie-groups and the Lie algebras, as well as the SU (2) and SU (3) groups. In order to present the Lie –group theory, definitions, suggestions and examples are given out. The fourth chapter deals with the Gauge Theories, the global and local transformations in the real and complex field of Klein-Gordon, the Yang-Mills field theory and the unification theory. Finally, the fifth chapter examines the spontaneous symmetry breaking, the Goldstone theorem and especially with the Higgs mechanism, explaining how the gauge bosons of the Standard Model acquire mass.

No description available.

We study complex analogues on Calabi-Yau manifolds of gauge theories on low dimensional real manifolds. In particular we define a holomorphic analogue of the Casson invariant, counting coherent sheaves on a Calabi-Yau 3-fold.