We develop a finite-temperature formulation for a hypercomplex dissipative quantum field theory [1], using the imaginary-time path-integral approach and the idempotent structure of the hypercomplex algebra. The resulting partition function naturally separates into two conjugate complex sectors whose recombination preserves the hypercomplex Hermitian structure while generating a nontrivial thermal phase. From this construction, the standard thermodynamic observables are obtained consistently, and the conventional relativistic charged Bose gas is recovered in the vanishing-dissipation limit. Beyond this equilibrium correspondence, the hypercomplex formulation reveals a distinctive perturbative hierarchy: dissipative effects first appear in the complementary phase sector, while corrections to ordinary real thermodynamic quantities arise only at higher order. These results show that dissipation can be encoded through an enlarged algebraic thermal structure without abandoning the familiar framework of relativistic finite-temperature field theory, opening a path toward broader applications of hypercomplex methods in dissipative, open, and effectively non-Hermitian quantum systems.
This graduate-level book is a coherent and self-contained introduction to quantum field theory (QFT), with a distinctive focus on geometric and nonperturbative aspects. The opening part covers quantum fields and the Euclidean path integral, Yang–Mills field theories, and Wilsonian renormalization. Wilson's notion of th...
We construct a finite-Hilbert interacting quantum model in which matter and geometric response are generated by a single Schwinger functional along one spatial refinement. Two inequivalent discretizations converge analytically to the same Hamiltonian on a fixed physical Fourier band, with second- and fourth-order regul...
In periodically driven open quantum systems, nonnormality renders the Floquet spectrum insufficient as the system approaches the thermodynamic limit, so that pseudospectra are needed to characterize the dynamics accurately. While conventional approaches mainly focus on the local dynamics of isolated pseudospectra, thei...
Yun-Cheng Xie, Hao-Zhe Shi, Zhuo-Cheng Ma et al.· 0 citations
Transitions out of non-Abelian topological order are difficult to describe in microscopic quantum models with numerical methods that remain tractable at large scales. We develop a sign-free path-integral framework for Kitaev quantum doubles $\mathcal D(G)$ by organizing single-link perturbations in terms of non-inverti...
R. Flores-Calderón, F. Pollmann, M. Knap· 0 citations
We develop a Hopf-algebraic theory of the graph coefficients arising in the quantum Magnus expansion. At the classical level, the graph expansion is governed by directed trees, whereas its quantum counterpart involves loop graphs, multiple edges, and different types of edge data. We introduce a contraction Hopf algebra...
Li Guo, Joon-Hwi Kim, Jung-Wook Kim et al.· 1 citation
We uncover a connection between the classical limit of the Magnus expansion in quantum field theory and the Malvenuto-Reutenauer Hopf algebra of permutations. We study a cubic scalar theory describing a massive particle coupled to massless scalar quanta, which captures the propagator structure relevant to classical sca...
A. Brandhuber, Graham R. Brown, Sebastien MacDonald et al.· 0 citations
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