Four main topics:

1. Baryon number violation through nonperturbative effects in the Electroweak Standard Model:

Sphalerons and spectral flow:

New results on spectral flow and sphalerons have been obtained [Klinkhamer & Lee, 2001], [Klinkhamer & Rupp, 2005] and are currently under investigation.

For two reviews, see [Klinkhamer, 2002], [Klinkhamer & Rupp, 2003].

2. CPT anomaly:

Chiral gauge theories defined over a topologically nontrivial space manifold have an anomalous breaking of Lorentz and CPT invariance. A recent review: [Klinkhamer, 2005]

• Exact results in 2D and 4D [Klinkhamer & Nishimura, 2001; Klinkhamer & Mayer, 2001; Klinkhamer & Schimmel 2002]

• Modified Maxwell theory [Klinkhamer & Adam, 2001-02; Kaufhold & Klinkhamer, 2005; Kant & Klinkhamer, 2005]:
  • microcausality
  • photon decay (γ → 3 γ)
  • birefringence

• Microscopic structure of spacetime [Klinkhamer & Rupp, 2003-2005]:
  • Spacetime foam affects photon propagation.
  • TeV photons from active galactic nuclei ⇒   l_foam < 1.6 × 10^-22 cm.

3. Quantum phase transition and neutrino oscillations:

A new type of quantum phase transition due to Fermi point splitting has been proposed [Klinkhamer & Volovik, 2004]. Such a quantum critical point may appear in the BEC-BCS crossover of ultracold gases of fermionic atoms (for example, Lithium-6 with p-wave pairing). More speculatively, there may be Fermi point splitting of the fermions of the Standard Model, which can be probed by neutrino-oscillation experiments [Klinkhamer, 2004-2006].

Neutrino-oscillation probabilities from a simple three-flavor model with both Fermi-point splittings Δb0(31) and mass-square differences Δm231. Top panels: P ≡ P(νμ → νe). Bottom panels: P'' ≡ P(νe → νμ). If CPT invariance holds, also P = P(anti-νe → anti-νμ) and P'' = P(anti-νμ → anti-νe). The probabilities are functions of the dimensionless parameters ρ ≡ (2 Eν) / (L |Δm231|) and τ ≡ L |Δb0(31)|, using natural units ℏ = c = 1 and for a neutrino beam with energy Eν and baseline L. Shown are constant–τ slices, where the heavy-solid curves in the two left panels correspond to τ = 0 (pure mass-square-difference model) and the other thin-solid, long-dashed, and short-dashed curves for positive τ correspond to τ = 1,2,0 (mod 3), respectively. These results show that there could be strong T–violating (and CP–violating) effects at the high-energy end of the neutrino spectrum from Fermi-point splitting or other emergent-physics dynamics.

4. Vacuum energy and cosmology:

Since 1998, it has become clear that there is not one cosmological constant problem but that there are three:

• Why is |ρ_vac| << (E_Planck)⁴ ?
• Why is ρ_vac ≠ 0 ?
• Why is now ρ_vac ∼ ρ_matter ?

Taking Lorentz-invariance seriously (cf. recent UHECR bounds on Lorentz violation in the photon sector [Klinkhamer, 2008]), a new approach [Klinkhamer & Volovik, 2008] to this set of problems is based on the following assumption:

the perfect quantum vacuum can be considered to behave as a self-sustained Lorentz-invariant medium with a new type of conserved charge.

The argument is based solely on thermodynamics (cf. Einstein 1907) and has an analog in condensed-matter physics (Larkin-Pikin effect, 1969).

Work is in progress on the expanding (and accelerating!) universe [Klinkhamer, 2008; Klinkhamer & Volovik, 2008].

1. Electroweak baryon number violation: basic mechanism (Ann Arbor, June 2003)
2. Nontrivial topology and CPT violation (Uppsala, September 2006)
3. Lorentz noninvariance and neutrino oscillations (Belgium, February/March 2006)
4. UHECR bounds on Lorentz violation in the photon sector (Penn State, August 2008)
5. Lorentz invariance, vacuum energy, and cosmology (Princeton, August 2008)
6. Brief introduction to q-theory and a QCD-scale modified-gravity universe (Tokyo, May 2010)
7. Towards a derivation of G (Bremen, July 2010)
8. Cosmological constant problem, q-theory, and new TeV-scale physics (Toronto, September 2010)
9. Cosmological constant and q-theory (Karlsruhe, March 2011)
10. Superluminal neutrino: Theoretical considerations (Karlsruhe, December 2011)