47,396 research outputs found
THE DYSON-SCHWINGER EQUATION FOR A MODEL WITH INSTANTONS - THE SCHWINGER MODEL
Using the exact path integral solution of the Schwinger model -- a model
where instantons are present -- the Dyson-Schwinger equation is shown to hold
by explicit computation. It turns out that the Dyson-Schwinger equation
separately holds for every instanton sector. This is due to Theta-invariance of
the Schwinger model.Comment: LATEX file 11 pages, no figure
Chern-Simons action for zero-mode supporting gauge fields in three dimensions
Recent results on zero modes of the Abelian Dirac operator in three
dimensions support to some degree the conjecture that the Chern-Simons action
admits only certain quantized values for gauge fields that lead to zero modes
of the corresponding Dirac operator. Here we show that this conjecture is wrong
by constructing an explicit counter-example.Comment: version as published in PRD, minor change
Integrable subsystem of Yang--Mills dilaton theory
With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2)
Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory
coupled to the dilaton. Here integrability means the existence of infinitely
many symmetries and infinitely many conserved currents. Further, we construct
infinitely many static solutions of this integrable subsystem. These solutions
can be identified with certain limiting solutions of the full system, which
have been found previously in the context of numerical investigations of the
Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the
integrable subsystem and show that our static solutions are, in fact, Bogomolny
solutions. This explains the linear growth of their energies with the
topological charge, which has been observed previously. Finally, we discuss
some generalisations.Comment: 25 pages, LaTex. Version 3: appendix added where the equivalence of
the field equations for the full model and the submodel is demonstrated;
references and some comments adde
Objectual understanding, factivity and belief
Should we regard Jennifer Lackey’s (2007) ‘Creationist Teacher’ as understanding evolution, even though she does not, given her religious convictions, believe its central claims? We think this question raises a range of important and unexplored questions about the relationship between understanding, factivity and belief. Our aim will be to diagnose this case in a principled way, and in doing so, to make some progress toward appreciating what objectual understanding—i.e., understanding a subject matter or body of information—demands of us. Here is the plan. After some ground clearing in §1, §2 outlines and motivates a plausible working model—moderate factivity—for characterising the sense in which objectual understanding should be regarded as factive. §3 shows how the datum that we can understand false theories can, despite initial suggestions to the contrary, be assimilated straightforwardly within the moderate factivity model. §4 highlights how the inverse kind of case to that explored in §3—viz., a variant of Lackey’s creationist teacher case—poses special problems for moderate factivity. With reference to recent work on moral understanding by Hills (2009), §5 proposes a solution to the problem, and §6 attempts to diagnose why it is that we might originally have been led to draw the wrong conclusion
Knowledge, Assertion and Intellectual Humility
This paper has two central aims. First, we motivate a puzzle. The puzzle features four independently plausible but jointly inconsistent claims. One of the four claims is the sufficiency leg of the knowledge norm of assertion (KNA-S), according to which one is properly epistemically positioned to assert that p if one knows that p. Second, we propose that rejecting (KNA-S) is the best way out of the puzzle. Our argument to this end appeals to the epistemic value of intellectual humility in social-epistemic practice
Googled Assertion
Recent work in the philosophy of mind and cognitive science (e.g., Clark and Chalmers 1998; Clark 2010a; Clark 2010b; Palermos 2014) can help to explain why certain kinds of assertions—made on the basis of information stored in our gadgets rather than in biological memory—are properly criticisable in light of misleading implicatures, while others are not
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