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Browsing by Subject "quantum field theory"

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  • Introduction to axiomatic quantum field theory in flat and curved spacetime 
    Garcia Sturba, Sebastian (2023)
    Quantum field theory is often presented without clearly defined mathematical structures, especially in the case of field operators. We discuss axiomatic quantum field theory, where quantum fields and states are defined rigorously using distribution theory, alongside their assumed properties in the form of the Wightman axioms. We present the two key results that come from this construction, namely CPT symmetry and the spin-statistics connection. We then consider the construction of quantum fields in curved spacetime so as to discuss their behaviour in regions of large curvature, such as near black holes. This requires us to redefine fields and states in terms of *-algebras. We then present the GNS reconstruction theorem which allows us to get back the original definitions of these objects in Minkowski spacetime.
  • Majorana neutrinos and their oscillations in QFT 
    Kupiainen, Tomi (2020)
    In this work we consider the method of unitarily inequivalent representations in the context of Majorana neutrinos and a simple seesaw model. In addition, the field theoretical framework of neutrino physics, namely that of QFT and the SM, is reviewed. The oscillating neutrino states are expressed via suitable quantum operators acting on the physical vacuum of the theory, which provides further insight to the phenomenological flavor state ansatz made in the standard formulation of neutrino oscillations. We confirm that this method agrees with known results in the ultrarelativistic approximation while extending them to the non-relativistic region.
  • Quantum circuit for a real-time dynamics simulation of the massive Gross-Neveu model 
    Enckell, Anastasia (2023)
    Numerical techniques have become powerful tools for studying quantum systems. Eventually, quantum computers may enable novel ways to perform numerical simulations and conquer problems that arise in classical simulations of highly entangled matter. Simple one dimensional systems of low entanglement are efficiently simulatable on a classical computer using tensor networks. This kind of toy simulations also give us the opportunity to study the methods of quantum simulations, such as different transformation techniques and optimization algorithms that could be beneficial for the near term quantum technologies. In this thesis, we study a theoretical framework for a fermionic quantum simulation and simulate the real-time evolution of particles governed by the Gross-Neveu model in one-dimension. To simulate the Gross-Neveu model classically, we use the Matrix Product State (MPS) method. Starting from the continuum case, we discretise the model by putting it on a lattice and encode the time evolution operator with the help of fermion-to-qubit transformations, Jordan-Wigner and Bravyi-Kitaev. The simulation results are visualised as plots of probability density. The results indicate the expected flavour and spatial symmetry of the system. The comparison of the two transformations show better performance of the Jordan-Wigner transformation before and after the gate reduction.

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