arXiv subjects
Publications and source records attributed to Christian Jaekel.
The relativistic KMS condition introduced by Bros and Buchholz provides a link between quantum statistical mechanics and quantum field theory. We show that for the $P(ϕ)_2$ model at positive temperature, the two point function for fields satisfies the relativistic KMS condition.
We consider the formal non relativistc limit (nrl) of the :ϕ^4:_{s+1} relativistic quantum field theory (rqft), where s is the space dimension. Following work of R. Jackiw, we show that, for s=2 and a given value of the ultraviolet cutoff κ, there are two ways to perform the nrl: i.) fixing the renormalized mass m^2 equal to the bare mass m_0^2; ii.) keeping the renormalized mass fixed and different from the bare mass m_0^2. In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as κ-> \infty in case i.) and, in case ii.), there is a bound state, indicating that the interaction potential is attractive. As a consequence, stability of matter fails for our boson system. We discuss why both alternatives do not reproduce the low-energy behaviour of the full rqft. The singular nature of the nrl is also nicely illustrated for s=1 by a rigorous stability/instability result of a different nature.
We establish a useful identity for intertwining a creation or annihilation operator with the heat kernel of a self-interacting bosonic field theory.
Given a thermal field theory for some temperature $β^{-1}$, we construct the theory at an arbitrary temperature $ 1 / β'$. Our work is based on a construction invented by Buchholz and Junglas, which we adapt to thermal field theories. In a first step we construct states which closely resemble KMS states for the new temperature in a local region $Ø_\circ \subset \rr^4$, but coincide with the given KMS state in the space-like complement of a slightly larger region $\hatØ$. By a weak*-compactness argument there always exists a convergent subnet of states as the size of $ Ø_\circ$ and $ \hatØ$ tends towards $ \rr^4$. Whether or not such a limit state is a global KMS state for the new temperature, depends on the surface energy contained in the layer in between the boundaries of $ Ø_\circ$ and $ \hatØ$. We show that this surface energy can be controlled by a generalized cluster condition.
We combine recent results of Clifton and Halvorson [1] with structural results of the author [2--5] concerning the local observables in thermofield theory. An number of interesting consequences are discussed.
We establish the Schlieder and the Borchers property for thermal field theories. In addition, we provide some information on the commutation and localization properties of projection operators.
We show that the Reeh-Schlieder property w.r.t. the KMS-vector is a direct consequence of locality, additivity and the relativistic KMS-condition. The latter characterises the thermal equilibrium states of a relativistic quantum field theory. The statement remains vaild even if the given equilibrium state breaks spatial translation invariance.
We construct interacting quantum fields in 1+1 dimensional Minkowski space, representing neutral scalar bosons at positive temperature. Our work is based on prior work by Klein and Landau and Hoegh-Krohn
We construct interacting quantum fields in 1+1 space-time dimensions, representing charged or neutral scalar bosons at positive temperature and zero chemical potential. Our work is based on prior work by Klein and Landau and Hoegh-Krohn. Generalized path space methods are used to add a spatially cut-off interaction to the free system, which is described in the Araki-Woods representation. It is shown that the interacting KMS state is normal w.r.t. the Araki-Woods representation. The observable algebra and the modular conjugation of the interacting system are shown to be identical to the ones of the free system and the interacting Liouvillean is described in terms of the free Liouvillean and the interaction.
Recently it has been shown that the Reeh-Schlieder property w.r.t. thermal equilibrium states is a direct consequence of locality, additivity and the relativistic KMS condition. Here we extend this result to ground states.
We review the heuristic arguments suggesting that any thermal quantum field theory, which can be interpreted as a quantum statistical mechanics of (interacting) relativistic particles, obeys certain restrictions on its number of local degrees of freedom. As in the vacuum representation, these restrictions can be expressed by a `nuclearity condition'. If a model satisfies this nuclearity condition, then the net of von Neumann algebras representing the local observables in the thermal representation has the split property.
The basic ingredients of Tomita-Takesaki modular theory are used to establish cluster estimates. Applications to thermal quantum field theory are discussed.
We study the cluster properties of thermal equilibrium states in theories with a maximal propagation velocity (such as relativistic QFT). Our analysis, carried out in the setting of algebraic quantum field theory, shows that there is a tight relation between spectral properties of the generator of time translations and the decay of spatial correlations in thermal equilibrium states, in complete analogy to the well understood case of the vacuum state.