Theoretical Bachelor Projects
Klaus Bering
February 24th, 2023
Theoretical Bachelor Projects
Q General remarks
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Theoretical diploma & PhD project?
• I do supervise them, but today I will focus on bachelor projects.
How to sign up?
• Come to my office.
• I sometimes have camera-ready projects, but usually the project topic is not fixed on the very first day, and is a result of what fits student and superviser best.
• Since many projects use Lagrangian or Hamiltonian formulations, my course F5500 Analytic Mechanics is recommended (possibly concurrently).
Theoretical Bachelor Projects
Q Topics in theoretical physics & previous bachelor students
Lagrangian & Hamiltonian formulations, symplectic geometry
o Ondrej Hulik: WKB approximation & Maslov index in QM. o Samuel Valach: Contact geometry (opponent).
Symmetry, group theory & conservation laws
• David Svoboda: QED Ward identity.
• Martin Skorna: Non-relativistic Goldstone theorem.
QM/QFT/path integral
• Michal Pazderka: Non-commutative QM & Seiberg-Witten map.
• Nikolas Masnicak: Casimir effect.
• Ondrej Kovanda & Radek Sláma: Batalin-Vilkovisky (BV) formulation of relativistic point particle.
• Jan Merta: Shor algorithm for quantum computers & number theory.
9 Matus Liptak: Schródinger equation solved via path integral.
String theory
9 Paulina Karlubikova: Regularize string oscillator modes to derive anomaly cancellation in D = 26 bosonic string theory.
Supermathematics
General relativity
• Tomas Michalik: General relativity modeled over the de-Sitter group SO(l,4).
• Darek Cidlinsky & Nino Lomtatidze: The mass parameter in the Schwarzschild solution has an interpretation as the total energy.
NB
• Just because a topic already became a thesis, it is usually far from exhausted.
Theoretical Bachelor Projects
0 Example: Schrodinger equation solved via path integral & Feynman diagrams
Example: Schrodinger equation solved via path integral & Feynman diagrams
Ongoing bachelor project with Matus Lipták
ID Schrodinger equation: Oscillator with cubic interaction
ft2 d2
+ %r*2 + gx3 ) il>{x) = Eq^(x).
2 dx2
r Perturbative	ground state	energy		
E° = 2	lift2 2 8u*g	465ft3 4 32uQ g	39708ft4 6 128w14 8	+ 0(g8)
Path integral			
44 = j	1          Vx exp < x(0)=x(T)		Í    dt (^X2 + yX2 + gX3 - Jx)\
Vacuum Feynman diagrams with symmetry factor 5
r2-loop: 0(g2)		
	o-o e S = 23             S = 2x3!	
r3-loop: 0(g4) J		
	S = 24                            S = 23 S = 24                S = 23x3!	
Děkuji!