We have built a constrained four-dimensional quaternion-parametrized conformal field theory using quaternion holomorphic functions as the generators of quaternionic conformal transformations. With the two-dimensional complex-parametrized conformal field theory as our model, we study the stress tensor, the conserved charge, the symmetry generators, the quantization conditions and several operator product expansions. Future applications are also addressed.

Holomorphic quaternion functions only admit affine functions; thus, the Möbius transformation for these functions, which we call quaternionic holomorphic transformation (QHT), only comprises similarity transformations. We determine a general group X which has the group G of QHT as a particular case. Furthermore, we observe that the Möbius group and the Heisenberg group may be obtained by making X more symmetric. We provide matrix representations for the group X and for its algebra x. The Lie algebra is neither simple nor semi-simple, and so it is not classified among the classical Lie algebras. We prove that the group G comprises SU(2,C) rotations, dilations and translations. The only fixed point of the QHT is located at infinity, and the QHT does not admit a cross-ratio. Physical applications are addressed at the conclusion.

A quaternionic analog of the Aharonov–Bohm effect is developed without the usual anti-hermitian operators in quaternionic quantum mechanics. A quaternionic phase links the solutions obtained to ordinary complex wave functions, and new theoretical studies and experimental tests are possible for them.

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In this chapter, I assess Spinoza’s explanation of his definition of desire at the end of the third part of the Ethics, wherein we find a peculiar expression: “causa conscientiae,” “the cause of consciousness” (E3deffaff1). Surprisingly, this phrase has not been taken into much consideration in the recent revival of interest in Spinoza’s view of this aspect of human experience.2 A careful study of this text will shed some fresh light on Spinoza’s general discussion of consciousness and provide a new answer to the question of why, according to Spinoza, philosophy ought not to start with the indubitable act of thinking of a self-conscious subject.3 This new answer, which differs from the usual – and also undoubtedly correct – one, makes no use of Spinoza’s conception of the true order of understanding, and therefore that of true philosophy, but relies rather on the sense and limits of the conception of consciousness that can be apprehended from the analysis of this passage.

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Bertrand Russell is widely known for his willingness to change his philosophical mind. He is also now and again saddled with a reputation for carelessness about providing readers with clear and convincing explanations of his turnabouts. This chapter presents and briefly assesses the development of Russell's thinking about memory, emphasizing, against the grain of the received view, the continuity in his thought. Russell's ideas about memory are no exception to that perceived pattern of progress. The core notion of the early theory is that of acquaintance, by which Russell means a mode of cognition which is both immediate and purely receptive. The main ostensible problem for the theory is that of accounting for retention—specifically, making sense of the idea of being now acquainted with what has been and is no more. The abandonment of direct realism should predictably bring about a further increase in Russell's concern over fallibility and error in memory.