The subject of this work time dependent solutions of the massless Gross-Neveu model. The Gross-Neveu model is a 1+1 dimensional field theory of N flavours of fermions with four-fermion interaction. In the limit of large flavour numbers N , this theory can be solved exactly by a mean field approximation equivalent to the Hartree-Fock method of relativistic many-particle physics. Nearly all solutions that have been found until now, like “kinks” and “DHN-baryons”, are time independent, since there exists a systematic way to generate such solutions. The only time dependent solution, the breather, has been found by guessing. In this thesis we present new time dependent solutions. Firstly, we show that a special case, the scattering of an arbitrary number of kinks, can be mapped onto an already solved problem. Secondly, we use the fact that Hartree-Fock potential and wave functions of the already known solutions can be written as fractions of polynomials of exponential functions. We make an ansatz of new polynomials, determine their coefficients via the Dirac equation and confirm the self consistency. That way we find analytic solutions for the scattering of up to four DHN-baryons or breathers and can even give a, yet unproven, formula for the scattering of an arbitrary number of such objects.The subject of this work time dependent solutions of the massless Gross-Neveu model. The Gross-Neveu model is a 1+1 dimensional field theory of N flavours of fermions with four-fermion interaction. In the limit of large flavour numbers N , this theory can be solved exactly by a mean field approximation equivalent to the Hartree-Fock method of relativistic many-particle physics. Nearly all solutions that have been found until now, like “kinks” and “DHN-baryons”, are time independent, since there exists a systematic way to generate such solutions. The only time dependent solution, the breather, has been found by guessing. In this thesis we present new time dependent solutions. Firstly, we show that a special case, the scattering of an arbitrary number of kinks, can be mapped onto an already solved problem. Secondly, we use the fact that Hartree-Fock potential and wave functions of the already known solutions can be written as fractions of polynomials of exponential functions. We make an ansatz of new polynomials, determine their coefficients via the Dirac equation and confirm the self consistency. That way we find analytic solutions for the scattering of up to four DHN-baryons or breathers and can even give a, yet unproven, formula for the scattering of an arbitrary number of such objects.

Feb 22, 20210 citations

Relativistic Many-Body Theory

Ingvar Lindgren

Springer series on atomic, optical, and plasma physicsJan 1, 201169 citations

Ising and Gross-Neveu model in next-to-leading order

Benjamin Knorr

We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalization group. Their critical behavior is of special interest in condensed-matter systems, in particular graphene. To derive the $\ensuremath{\beta}$ functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudospectral methods to guarantee high accuracy. New estimates of critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalization-group studies of the same level of approximation. By contrast, the approximation for the Gross-Neveu model retains many more operators than all earlier studies. For two Dirac fermions, the results agree with both lattice and large- ${N}_{f}$ calculations, but for a single flavor, different methods disagree quantitatively, and further studies are necessary.We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalization group. Their critical behavior is of special interest in condensed-matter systems, in particular graphene. To derive the $\ensuremath{\beta}$ functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudospectral methods to guarantee high accuracy. New estimates of critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalization-group studies of the same level of approximation. By contrast, the approximation for the Gross-Neveu model retains many more operators than all earlier studies. For two Dirac fermions, the results agree with both lattice and large-${N}_{f}$ calculations, but for a single flavor, different methods disagree quantitatively, and further studies are necessary.

arXiv:1609.03824Physical review. B./Physical review. BDec 1, 201660 citations

Non-Relativistic Many-Body Perturbation Theory

Ingvar Lindgren

NATO ASI series. Series B : PhysicsJan 1, 19860 citations

Relativistic Effects in Many-Body Systems

Lloyd Armstrong

Springer eBooksJan 1, 19831 citation

{N}_{f}

calculations, but for a single flavor, different methods disagree quantitatively, and further studies are necessary.