PHYSICS REPORTS (Review Section of Physics Letters) 187, No. 3 (1990) 109—143. North-Holland JUSTIFYING THE CHIRAL BAG Linas VEPSTAS* Service de Physique Theorique, CEN-Saclay, 91190 Gil -sur-Yvette, France and A.D. JACKSON Department of Physics, State University of New York at Stony Brook, Stony Brook, NY 11794, USA Received June 1989 Contents: 1. Introduction 111 6. A different class of regulators 128 2. Casimir energy: the MIT bag interior 113 7. Reintroducing the mesonic effective Lagrangian 131 3. The MIT bag exterior 115 7.1. Cutting out low energies 131 4. The chiral bag interior 117 7.2. Cutting out high energies 135 5. The chiral bag exterior 122 7.3. The Cheshire Cat redux 137 5.1. The phase shift 123 8. Conclusions 139 5.2. Integrals over the phase shift 125 Appendix 140 5.3. The axial current 127 References 143 Abstract We show that the Casimir energy in the Chiral Bag Model, known to be divergent, becomes finite when exterior fermions are included. If limited to high energies, these fermions do not spoil the confinement properties of the bag. The result of finiteness is analogous to known results for the electromagnetic field in the presence of a thin conducting shell. Implications for the Cheshire Cat principle are examined, a justification for previous Chiral Bag Model calculations is offered, and new methods for simplifying Chiral Bag Model calculations are discussed. * Current address: IBM, 11400 Burnet Road, Austin, TX 78758, USA. Single orders for this issue PHYSICS REPORTS (Review Section of Physics Letters) 187, No. 3 (1990) 109—143. Copies of this issue may be obtained at the price given below. All orders should be sent directly to the Publisher. Orders must be accompanied by check. Single issue price Dfi. 27.00, postage included. 0 370-1573/90/$12.25 © Elsevier Science Publishers B.V. (North-Holland)